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B.A. (Hons) Economics-Ist Year
Paper – III
STATISTICAL METHOD FOR ECONOMICS
QUESTION BANK 2010-11
SHIVAJI COLLEGE
HOUSE EXAMINATION – 2011
1.
(a)
If the first three moments about the origin for a distribution are
10, 225 and 0 respectively. Calculate the first three moments
about the value 5 for the distribution.
(b)
Karl Pearson’s measure of skewness of a distribution is 0.5. The
median and mode of the distribution are respectively, 42 and
32. Find (i) Mean, (ii) standard deviation, (iii) coefficient of
variation.
(c)
Prove that A.M.  G.M.  H.M.
OR
(d)
(i)
The first four moments of a distribution about a value 3 of
the variable are 2, 10 and 30 respectively. Do you think
that the distribution is leptokurtic?
(ii)
A student received a mark of 84 on a final examination in
economics for which the mean marks was 76 and
standard deviation was 10. On the final examination in
physics for which the mean marks was 82 and standard
deviation was 16, he received a mark of 90. In which
subject was his relative standing higher?
(e)
Calculate the Quartile Deviation and Coefficient of skewness
from the following data Q 2 = 188.8”. Q1 = 14.6” and Q3 = 25.2”.
Also indicate the nature of the distribution.
(f)
The mean and standard deviation of 100 observations were
found to be 60 and 10 respectively. At the time of calculations,
two items were wrongly taken as 5 and 45 instead of 30 and 20.
Calculate the correct mean and correct coefficient of variation.
2.
(a)
(i) Given P (A) = 0.59., P (B) = 0.30, and P A  B = 0.21., Find (i)
P A  B'
(ii) P A' B' and (iii) P A' B'
(ii) If a random variable X is normally distributed with mean μ
(b)
and variance σ 2 , show that the mean of the variable Z = X - μ / σ
is always zero and variance is one.
(i) A firm produces steel pipes in 3 plants with daily production
volumes of 500, 1000 and 2000 units respectively. According to
the past experience, it is known that fraction of defective output
produced by the 3 plants are respectively .005, .008 and .10. If
a pipe is selected from a day’s total production and found to be
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B.A. (Hons) Economics-Ist Year
(c)
(d)
(e)
Paper – III
defective, what is the probability that it came from the first
plant?
(ii) A box of fuses contains 20 fuses, of which five are defective.
If three of the fuses are selected at random and removed from
the box in succession without replacement, what is the
probability that all the three fuses are defective?
(i) The following table provides a probability distribution of the
random variable X.
X:
2
4
7
8
P(X) 0.2 0.3 0.4 0.10
Find (i) Var (X) (ii) If Y = 4X – 1 find Var (Y)
(ii) For a normally distribution variable X, what proportion of the
observations would be found between μ - σ and μ - 3σ ?
OR
(i) The time needed to complete a final examination in a
particular examination in a particular course is normally
distributed with a mean 80 minutes and a standard deviation of
10 minutes.
(a) What is the probability of completing the exam in one hour
or less?
(b) What is the probability that a student will complete the exam
in more than 60 minutes but less than 75 minutes?
(c) Assume that class has 60 students and the examination
period is 90 minutes in length. How many students do you
expect will be unable to complete the exam in the allotted
time?
(ii) For a binomial distribution of defective bolts, the probability
of defective bolts is given to be 0.2 and n is 500. Find the mean
and standard deviation of the distribution.
(i) An Institute surveyed 1000 students ages 16-22 about their
personal finance. The survey found that 33% of the students
have their own credit card.
(a) In a sample of 6 students, what is the probability that at
least two will have their own credit card?
(b) In sample of 6 students majority of students will have
their own credit card?
(ii) The joint distribution of X and Y is as follows:
X
-2
-1
0
1
2
Y
10
.09 .15 .27 .25 0.04
20 .01 .05 .08 .05 0.01
(a) Find the marginal distributions of X & Y.
(b) Find the conditional distribution of X given y = 20
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3.
(a)
(b)
(c)
(a)
Paper – III
(c) Find the conditional distribution of Y given x = 2
You are given below the following information about
advertisement and sales:
Adv. Exp. (x)
Sales (y)
(in crores of Rs.) (in crores of Rs.)
Mean
20
120
S.D.
5
25
Correlation coefficient (r) = 0.8
Find (i) Calculate two regression equations. (ii) Find the likely
sales when advertisement expenditure is Rs. 25 crores. (iii)
Standard error of estimate of regression Y on X.
Prove that coefficient of correlation lies between – 1 and + 1.
Given r 2  0.98, SX  26.67, SY  17.78, for 8 pairs of observation
calculate
(i) Regression coefficient b YX and b XY
(ii) 95% confidence interval for population regression coefficient
β
(iii) Test the significance of β at 5% level of significance.
OR
For a given set of a bivariate data, the following results were
obtained:
 X 190,  Y  20, n = 20,  x 2  20,  y2  90,  xy 100,
where x and y are deviations from respective means. Find:
(i)
Two regression equations.
(ii)
Obtain the standard error of estimate Y on X.
(iii) Test the significance of β at 5% level of significance.
(b)
(c)
For a regression of Y on X, the total sum of squares was found
to be 800 and the explained sum of squares was 392. If the
regression was based on 20 pairs of values, find:
(i)
Coefficient of determination.
(ii)
Standard error of estimate for the regression.
Data on advertising expenditures and revenue (in thousands of
dollars) for the Delhi Seasons Restaurant follow.
Advertising Expenditure (x):
1
2
4
6
10 14 20
Revenue (y):
19 32 44 40 52 53 54
(i)
Estimate the regression line Y on X.
(ii)
Find the predicted revenue earnings if the advertisement
expenditures is 30.
(iii) Did the estimated regression equation provide a good fit?
Explain.
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Paper – III
MH
B.A (HONS) ECONOMICS IST YEAR 2010-2011
1.
(a)
Prove that the standard deviation is independent of change of
origin but not of scale.
(b)
For a distribution, the first four moments about zero are 1,7,38
and 155 respectively. Compute the moment coefficient of
skewness and kurtosis. Also, comment on the nature of the
distribution.
(c)
If the price of a commodity doubles in a period of 4 years, What
is the average annual percentage increase?
Or
(a)
Find out the weighted harmonic mean of the first n natural
numbers where the weights are equal to the corresponding
numbers.
(b)
The first four central moments are given as 0, 4, 8 and 144.
Comment on the nature of the distribution.
(c)
The arithmetic mean of two observations is 127.5 and their
geometric mean is 60. Find their harmonic mean and the two
observations.
2.
(a)
In 4 years, the prices of oil were $0.8, $0.9, $ 1.05 and $1.25
per gallon. What is the average price for this period is $1000
was spend every year?
(b)
You are given the following probability distribution of X
X 1
2
3
4
5
6
P(X)
0.1
0.15
0.2
0.25
0.18
K
(c)
(a)
(b)
(i)
What is the value of k
(ii)
What is E(X) and V(X)?
(i) Find the probability of getting the sum 7 on atleast 1 of 3
tosses of a pair of fair dice.
(ii) How many tosses are needed in order that probability in (i) is
greater than 0.95?
Or
If you spend Rs. 100 per week on apples and the price of apples
for 3 weeks is Rs.25, Rs.20 and Rs. 10 per kg respectively, what
is the average price of apples for you?
In the following probability distribution, X and Y can take the
values 1, 2 and 3.
X
Y
1
2
3
1
2
3
5k
K
3k
4k
3k
4k
2k
3k
2k
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(c)
3.
(a)
(b)
(c)
(a)
(b)
(c)
4.
(a)
Paper – III
(i)
What is the value of k?
(ii)
Calculate E(X) and V(X)
Suppose that a central university has to form a committee of 5
members from a list of 20 candidates out of whom 12 are
teachers and 8 are students. If the members of the committee
are selected at random, what is the probability the majority of
the committee members are students?
Small cars get better gas mileage but they are not as safe as
bigger cars. Assume the probability of a small car being involved
in an accident is 0.18. The probability of an accident involving a
small car leading to a fatality is 0.128 and the probability of an
accident not involving a small car leading to a fatality is 0.5.
Suppose you learn of an accident involving a fatality, what is
the possibility a small car was involved?
A machine produces an average of 20% defective bolts. A batch
is accepted if a sample of 5 bolts taken from that batch contains
no defective and rejected if the sample contains 3 or more
defective. In other cases, a second sample is take. What is the
probability that the second sample is required?
In a large institution, 2.28% of the employees receive income
less than Rs.4500 and 15.8% of the employees receive income
more than Rs.7500 per month. Assuming incomes to be
normally distributed, calculate X and σ of the distribution
Or
Research shows that 30% of doctors in government hospitals
leave their jobs to start their own practice. Among those who
leave their jobs. 60% have a higher degree in specialization
while 20% of these who do not leave have a higher degree. If a
doctor has a specialization, what is the probability he will leave
his job to start a private practice?
Assuming that it is true that 2 in 10 industrial accidents are
due to fatigue, find the probability that
(i)
Exactly 2 of 8 industrial accidents will be due to fatigue.
(ii)
atleast 2 of 8 industrial accidents will be due to fatigue
The marks of a student in a certain examinations are normally
distributed with mean marks as 40% and standard deviation as
20%. 60% of the students failed. The result was moderated and
70% students passed. Find the pass marks before and after the
moderation.
The S.D in the amount of time it takes to train a worker to
perfume a tax is 40 mins. A random sample of 64 workers is
taken.
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(b)
(a)
(b)
5.
(a)
(i) What is the probability that the sample mean will exceed the
population mean by more than 5 mins?
(ii) What is the probability that the sample mean is more than 8
mins. Less than the population mean?
A radio shop sells, in an average 200 radios per day with a S.D
of 50 radios. After an extensive advertising campaign, the
management will compute the average sales for next 25 days to
see whether an improvement has occurred. Assume that the
daily sale of radio is normally distributed.
(i) Test the hypothesis at 5% level of significance if X = 216.
(ii) How large must X be in order that the null hypothesis is
rejected at 5% level of significance?
Or
A random sample of 81 purchased at a department store was
take to estimate the mean of all purchases. The population S.D
is $25.
(i)
What is the probability that the sample mean will not
overstate the population mean by more than $4?
(ii)
What is the probability that the sample mean will
understate the population mean by more than $1?
Cars running on normal petrol have an average engine life of
1,20,000 kms with a S.D of 15,000 kms. A random sample of
100 cars using premium petrol reported mean engine life of
1,22,000 kms.
(i)
Test whether premium petrol increases car engine life
using α = 0.05.
(ii)
What is the highest value of α that allows you to conclude
that the engine life improves with the use of premium
petrol?
The following table shows how a sample of Maths and Statistics
scores of 25 students are distributed.
Maths
(b)
Paper – III
40–70
70–100
Statistic
40–70
5
2
70–100
7
11
Test at 5% level of significance whether scores in Maths and
Statistics obtained by students are related.
In a sample of 100 bulbs, the mean lifetime was found to be 100
hrs. with a S.D of 200 hrs. In another sample of 100 bulbs, the
mean and S.D. were 1200 hrs & 100 hrs. respectively. Could
they have come from the sample population? Use α = 0.05
Or
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(a)
(b)
Paper – III
The scientific experiment with peas revealed the following
observations -315 round and yellow, 108 round and green, 101
wrinkled and yellow and 32 wrinkled and green. According to a
previous theory, the numbers should be in proportion 9:3:3:1. Is
there any evidence to doubt the theory at 1% and 5% level of
significance?
In a sample of 1500, the mean and S.D are found to be 18.5
and 4.5 respectively. In another sample of 1000, the mean is 20
and S.D is 4. Assuming that the sample s are independent, can
they arise from the same population? Use α = 5%
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B.A. (Hons) Economics-Ist Year
Paper – III
SATYAWATI COLLEGE (EVE.)
MID-TERM EXAMINATION – 2010-11
1.
(a)
Cities A, B and C are equidistant from each other. A motorist
travels from A to B at 30 miles/hr, from B to C at 40 miles/hr,
and from C to A at 50 miles/hr. Determine his average speed for
the entire trip.
(b)
The first four moments of a distribution about 3 are 1, 3, 6, and
8. Is the data consistent? Explain.
(c)
Prove that variance of first “n” natural numbers is n 2  1 /12.
Or
(a)
The first four moments of a distribution about value 4 are -1.5,
17, -30 and 108 respectively. Calculate four moments about
mean, β1 and β 2 Comment on nature of the distribution.

(b)
(c)
2.
(a)
(b)
(c)
(a)
(b)

Prove that A.M.  G.M.  H.M. taking positive observations a &
b.
The mean and variance of 10 observations are known to be 17
and 33 respectively Later it is found that one observation (i.e.
26) is inaccurate and is removed. What is the man and standard
deviation of the remaining observations?
Suppose that a Central University has to form a committee of 5
members from a list of 20 candidates out of whom 12 are
teachers and 8 are students. If the members of the committee
are selected at random, what is the probability that the majority
of the committee members are students?
“A frequency distribution can be described almost completely by
the first four moments and the two measures based on
moments.” Examine the statement
What is the chance that a leap year selected at random will
contain 53 Sundays?
Or
A factory has two machines, X and Y. Empirical evidence has
established that machines X and Y produce 30% and 70% of the
output respectively. It has also been established that 5% and
1% of the output produced by these machines respectively was
defective. A defective item is drawn at random. What is the
probability that the defective item was produced by machine X?
The IQ’s of army volunteers in a given year are normally
distributed with μ = 110 and σ = 10. The army wants to give
advance training to the 20% of those recruits with the highest
scores. What is the lowest IQ score acceptable for advanced
training?
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3.
(a)
(b)
(c)
(a)
Past experience indicates that 60% of the students entering
college get their degrees. Using the normal approximation to
binomial, find the probability that out of 30 students picked at
random from entering class, more than 20 will receive their
degrees
Assume that the family incomes are normally distributed with
μ = Rs 16000, and σ = Rs 2000. What is the probability that a
family picked at random will have an income i) between Rs.
15000 and Rs. 18000, ii) Below Rs 15000, iii) Above Rs 18000
and iv) Above Rs 20000?
If the random variable X is normally distributed with mean μ
and variance σ 2 derive the mean and variance of the variable z =
x  μ /σ .
Define with suitable examples. (i)A random variable, (ii) A
discrete random variable, (iii) A continuous random variable.
Or
What is a Normal distribution and what is its usefulness. How
is it different from a Standard Normal distribution? Explain with
suitable diagrammatic illustrations.
Prove the following:
(i)
E (aX + b) = aE (X) + b
(ii)
E (X + c) E (X) + c
(iii)
(b)
(c)
(a)
(b)
(c)
Paper – III
 
Var (X) = E X 2 - E X 
2
Where X is a random variable and a, b, & c are constants
The completion times for a job task range from 10.2 minutes to
18.3 minutes and are thought to be uniformly distributed. What
is the probability that it will require between 12.7 and 14.5
minutes to perform this task.
Distinguish between independent and mutually exclusive
events. When will the events be both independent are mutually
exclusive?
Find the probability of getting the sum 7 on at least 1 out of 3
tosses of a fair dice. How many tosses are needed in order that
such probability is greater than 0.95?
Or
The lifetime of light bulbs is known to be normally distributed
with μ = 100 hrs and σ = 8 hrs. What is the probability that a
bulb picked at random will have a lifetime between 110 and 120
burning hours.
What is the probability of: (a) two 6s on 2 rolls of a die, (b) a 6
on each die on rolling two dice once, (c) 3 girls in a family with 3
children.
Discuss the axioms of probability with suitable examples.
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4.
(a)
(b)
(c)
(a)
(b)
(c)
Paper – III
Show that Laspeyre’s Price Index can be written as a weighted
average of price relatives. What are the weights?
An index number is at 100 in year 2001. It rises by 4% in year
2002, falls by 6% in 2003, falls 4% in 2004 and rises 3% in
2005. Calculate index number for five years with 2003 as base.
The Consumer Price Index over a certain period increased from
110 to 200 and the salary of the workers increased from Rs
3,500 to Rs 5000. What is the gain or loss to the workers?
Or
Explain time reversal, factor reversal and circular tests.
Examine whether Laspeyre’s and Paasche’s index numbers
satisfy these tests.
Given the two price index series, splice them on the base 2004 =
100. By what percent did price of steel rise between 2000 and
2005
YEAR
Old Price Index New Price Index
Base 1995 = 100
Base 2004 = 100
2000
141.5
2001
163.7
2002
158.2
2003
156.8
2004
157.1
100.0
2005
102.3
The consumer price index for a group of workers was 250 in
2004 with 1990 as the base:
(i)
Compute the purchasing power of a rupee in 2004
compared to 1990.
(ii)
At what value of Consumer Price Index would the
purchasing power of a Rupee be 25 paisa.
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Paper – III
KALINI COLLEGE
HALF – YEARLY EXAMINATION 2010-2011
1.
(a)
Given the first four moments of a distribution μ 1 = 0, μ 2 = 40,
μ 3 = -100, μ 4 = 200, test the skewness and kurtosis of the
distribution.
(b)
Find mean and S.D. of the following observations:
X: 1, 2, 4, 8, 9.
Transform the above observations such that the mean of the
transformed observation becomes double of the mean of X, std.
Remaining unchanged.
OR
1.
(a)
an income tax assesse depreciated the machinery of his factory
by 20% in each of the first 2 years and 40% in the third year.
How much average depreciation relief should he claim from the
taxation department?
(b)
The first four moment of a distribution about the value 5 of the
variable are 2, 20, 40 and 50 show that the mean is 7, variance
16 and μ 3 = -64.
2.
(a)
Does a zero value of Karl Pearsons co-efficient of correlation
between two variable X&Y imply that X&Y are not related
explain.
(b)
What is the co-efficient of determination. How is it useful in
interpreting the value of an observed correlation. Given by.x = 1.4 & bxy = -0.5 calculate the coefficient of correlation &
interpret the result.
(c)
The co-efficient of correlation between the two variable X&Y is
0.48. The covariance Is 36. The variance of X is 16. Find the
Std. Dev of Y.
OR
2.
(a)
The correlation co-efficient between eh two variables X & Y is
found to be 0.4. What is the correlation between 2X & (-Y).
(b)
If the correlation co-efficient between the annual value of
exports & the annual No. of children born during the last ten
years is + 0.9, what inference if any, would you draw.
(c)
Family income and its percentage spent on food in the case of
hundred families gave the following bivariate frequency
distribution. Calculate the coefficient of correlation and
interpret its value.
Food
Family income (Rs.)
Expenditure
(in %)
200-300
300-400 400-500 500-600 600-700
10-15
–
–
–
3
7
15–20
–
4
9
4
3
20–25
7
6
12
5
–
25–30
3
10
19
8
–
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3.
(a)
(b)
(c)
(d)
(e)
(f)
3.
(a)
(b)
(c)
Paper – III
‘Mutual independence and mutual exclusiveness are not
synonymous’. Prove.
It is given that PA  B = 5/6, PA  B = 1/3 and P(B) = ½ show
that A & B are independence events.
What do you understand by a random variable and its
probability distribution? Define mathematical expectation of a
random variable.
Time taken by the crew of a company to construct a small
bridge is a normal variate with mean 400 labor hours and
standard deviation of 100 labor hours.
(i)
What is the probability that the bridge gets constructed
between 300 to 450 labour hours?
(ii)
If the company promises to construct the bridge in 450
labour hours or less and agrees to pay a penalty of Rs.
100 for each labour hour spent in excess of 450. What is
the probability that the company pays a penalty of at least
Rs. 2000.
If the probability of a defective bolt is 0.1, find (i) the mean and
(ii) the standard deviation for the distribution of defective bolt in
a total of 400.
Two sets of candidates compete for positions of Board of
Directors of a company. The probabilities for winning are 0.7 &
0.3 for the two sets. If the first set wins they will introduce a
new product with a probability 0.4. Similarly value for the
second set is 0.8. If the new product was introduced, what is
the chance that the first set was as directors.
Or
A piece of electronic equipment has tow essential parts A&B. In
the past, part A failed 30% of the time, part B failed 20% of the
time and both parts failed simultaneously 5% of the times.
Assuming that both part must operate to enable the equipment
of function. What is the probability that the equipment will
function.
A state commission has been found to reduce response time of
local fire departments. A group of experts is attempting to
identify these city fire department whose response time is either
in the lowest 10 percent or who take longer than 90 percent of
all fire department in the study. Those in the first group are to
serve as models for the less efficient fire units in the second
group.
Data show that the mean response time for a certain class of
fire department is 12.8 minutes, with a standard deviation of
3.7 minutes.
Obtain the variance of the binomial variate X show that V (cx)=
C 2 V(x) where C is constant.
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(d)
(e)
4.
(a)
(b)
(c)
(d)
4.
(a)
(b)
(c)
(d)
(e)
Paper – III
Assuming that each child has probability 0.4 of being a boy,
find the probability distribution of number of boys in a family of
4 children. In a sample of 500 couples how many do vou expect
to have (i) at least one boy (ii) exactly one girl.
The median of a frequency distribution if 89.0 and the first
quartile is 75.5. Find the Std. Dev. Assuming that the
distribution is normal.
Distinguish between mull and alternate hypotheses. State the
null and alternate hypotheses regarding population mean that
lead to (i) left tailed test and (ii) two tailed test. Explain clearly
why hypotheses of Ho : μ  10 requires a right tailed and μ 
10 requires a left tailed test.
Explain the concept of confidence level and confidence
coefficient. Give the critical value of z corresponding to 95% and
99% confidence level for one tailed test.
Define simple random sampling with replace3ment (srswr).
What do you know about the Sampling Distribution of the
sample mean when sampling is srswr. What do you know about
its standard error
A Stenographer claims that she can take dictation at the rate of
120 words per minute. Can we reject her claim on the basis of
100 trials in which she demonstrates a mean of 116 words with
a std.dev. Of 15 worlds? Use 5% level of significance & 1% level
of significance.
OR
With the help of the diagrams, Explain Type 1 and Type 11
errors.
A population consists of three numbers 2, 4, 6. Consider all
possible sample of size two without replacement. Show that the
variance of sampling distribution of means is less than the
variance of the population.
A random sample of 400 items is found to have a mean of 82
and S.D. of 18. Find 95% confidence limits for the mean of the
population from which the sample is drawn.
A man buys 50 electric bulbs of ‘Philips’ and 50 electric bulb of
‘HMT’. He finds that Philips bulbs give an average life of 1500
hrs. with S.D. of 60 hrs. and HMT bulbs give an average life of
1512 hrs. with a S.D. of 80 hrs. Is there a significant difference
in the mean life of the two makes of bulb?
Distinguish between (a) point estimation and interval estimation
or a parameter and a statistic.
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B.A. (Hons) Economics-Ist Year
Paper – III
DAULAT RAM COLLEGE
HOUSE EXAMINATIONS (JAN’,2011)
1.
(a)
Employee dissatisfaction at ‘Bates Electronics’ is reflected in the
number of official complaints over the past four months: 23, 41,
37 and 49. Based on this data, what is the average monthly
increase in complaints?
(b)
The shareholders research centre of India has conducted a
research study on price behavior of three leading industrial
shares ‘P’, ‘Q’ and ‘R’ for the period 2000-2005, the results of
which are published in its quarterly journal:
Share
Average Price S.D. (  ) (Rs.)
Current
(Rs.)
Selling
Price
(Rs.)
P
18.0
5.4
36.00
Q
22.5
4.5
34.75
R
24.0
6.0
39.00
Which share appears to be more stable in value. Which one would you
like do dispose of at present and why? (Given that you are a holder of
all three shares.)
(c)
The first four moments of a distribution about 3 are 1,3,6 and
8. Is the data consistent? Explain.
OR
(c)
Of a total of ‘N’ numbers, the fraction ‘P’ are ones and the
fraction q = 1-p are zeros. Find the moment coefficient of
skewness and kurtosis.
OR
1.
(a)
A large firm selling sports equipment is testing the effect of two
advertising plans on sales over the last four months.
Given the sales seen here, which advertising program seems to
be producing the highest mean growth in monthly sales?
Month
Plan-1
Plan-2
January
Rs. 1657.00
Rs. 4735.00
February
Rs. 1998.00
Rs. 5012.00
March
Rs. 2267.00
Rs. 5479.00
April
Rs. 3432.00
Rs. 5589.00
(b)
The following table gives the length of life of 400 radio tubes:
Length of life (hour)
No. of radio tubes
1000–1199
12
1200–1399
30
1400–1599
65
1600–1799
78
1800–1999
90
2000–2199
55
2200–2399
36
2400–2599
25
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B.A. (Hons) Economics-Ist Year
2
2.
Paper – III
2600–2799
9
Calculate the percentage number of tubes where length of life of tube
falls within X  2σ Compare with the theoretical result.
(c)
Given that the mean of a distribution is 5, variance is 9 and
moment coefficient of skewness is – 1. Find the first three
moments about the origin.
Or
(c)
Given that the mean of the distribution is 50 and mode is 58 :(i) Calculate the median
(ii) What can you day about the shape of the distribution?
Explain.
(a)
Distinguish between independent and mutually exclusive
events. When will the events ‘A’ and ‘B’ be both independent and
mutually exclusive?
(b)
The employees of a firm are classified according to length of
service with the firm (X) and salary grade (Y). There are three
grades 1, 2 and 3, grade ‘1’ being the lowest and grade ‘3’ the
highest. The results for the firm’s 200 employees are
summarized by the following joint frequency table.
Length of
Solary Grade (Dollars
Total
Service
Y
(Years) X
1
2
3
1
20
0
0
20
2
40
10
0
50
3
24
24
12
60
4
16
26
8
50
5
0
0
20
20
From the data contained in this table:
(i) Construct a bivariate probability table, showing the marginal
distribution of ‘X’ and ‘Y’.
(ii) Find the conditional probability distributions of ‘Y’ for the
given values of ‘X’. Are ‘X’ and ‘Y’ statistically independent?
(c)
If the random variable ‘X’ is normally distributed with mean ‘ μ ’
x - μ  is
and variance σ 2 , Show that the mean of the variable Z 
σ
always zero?
Or
(a)
Each of three identical jewelry boxes has tow drawers. In each
drawer of the first box, three is a gold watch. In each drawer of
second box, there is a silver watch. In one drawer of the third
box, there is a gold watch while in the other, there is a silver
watch. If we select a box at random. Open one of the drawers
and find it to contain a silver watch, what is the probability that
the other drawer has the gold watch.?
(b)
The mean weight of 500 male students at a certain college is
151 1b and the standard deviation is 151 1b. Assuming that
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Ravinder N. Jha
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B.A. (Hons) Economics-Ist Year
3.
3.
Paper – III
weights are normally distributed, find how many students
weight (i) between 120 and 155 1b (ii) more than 185 1b.
Or
(b)
What do you understand by a random variable? A random
variable has the following probability distribution:
Value of X: 0
1
2
3
Probability: 0.1 0.3 0.4 0.2
Find:
(i) E (X)
(ii) Var (X)
(c)
Cans of Happy – Tale dog Food average 16 ounces, with a range
of 4.2 ounces.
(i) What is the smallest can in ounces that one can buy for
weiner a toy poodle? What is the largest can one can buy for
wolfhound a killer?
(ii) If one picks a can at random, what is the probability it will
weigh between 15.8 and 16.5 ounces?
(a)
During a certain period the consumer price index increased
from 110 to 200 and salary of a worker also increased from Rs.
3500 to Rs. 5000. What is the real if any to the worker?
(b)
If Laspeyre’s price index is equal to paasche’s index show that
paasche’s index number will satisfy the time reversal test?
Or
(a)
Show that in general, the laspeyre’s price index is greater than
the passche’s index. When would this not be so?
(b)
The following data relate to the average weekly income of
workers and the price index:
Year
Weekly Income (Rs) Price Index (Rs.)
(1995=100)
1995
800
100
1996
819
105
1997
825
110
1998
876
120
1999
920
125
2000
924
135
Calculate the real income of the workers during the years 1995-2000.
*****
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