Download Homework11-Probability Distributions-Due date 4/13/05

Business Mathematics I
Homework 11
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Math 115a, Section:
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1.(Exercise 5 in Probability Distributions) Let X be a finite random variable with the
following p.m.f., f X .
x
f X (x)
1
0.1
2
0.3
3
0.4
4
0.2
Find all values for FX (x) . Hint: You will need to list the values by ranges, such as
1 x  2.
2. The c.d.f., FY (y) , of a finite random variable, Y, is given below.
0
0.05

0.25
FY ( y )  
0.65
0.85

1.00
if
if
if
if
if
if
y0
0 y2
2 y6
6  y  12
12  y  20
y  20
(i) What are the possible values of Y? (ii) Find all values of f Y ( y) .
3. Let X be the number of heads in a sequence of four independent tosses of a fair coin.
Find all values for FX (x) .
4. (Exercise 11 in Probability Distributions) Suppose in Example 2, the probability of
one call being handled correctly is changed to 0.7. Use BINOMDIST to compute the
probability that at most nine calls out of a set of 14 calls are handled correctly.
5. Let Y be a binomial random variable with n  15 and p  0.8 . Use BINOMDIST to
compute P(Y  12) .
6. (Exercise 17 in Probability Distributions) Let X be the continuous random variable
whose p.d.f., f X , is used in Density 1.xls. Use that file to find P( X  3.83) .
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7. (Exercise 18 in Probability Distributions) A packing plant uses a 120′ conveyor belt to
move filled cans to the crating area. When a can falls off of the belt it is equally likely to
do so at any point along the route. Let X be the distance, in feet, from the start of the belt
to the point where the next can falls off of the belt. Assuming that X has a uniform
distribution, find a formula for FX (x) and use this to compute the probability that the
can falls off at a point between 40′ and 85′ from the start of the belt.
8. (Exercise 21 in Probability Distributions) Buyers often insist on discounts for large
orders. Experience shows that the amount of their required discounts ranges from 0 to
18%, with a uniform distribution. (i) If D is the random variable giving the percent
discount, find a formula for f D (d ) and use this to compute the probability that a new
buyer will expect a discount that is between 5% and 12%.
9. (Exercise 27 in Probability Distributions) Let X be an exponential random variable
with parameter   3.5 . (i) What is the probability that X takes a value of at least 4? (ii)
What is the probability that X takes a value of at most 4?
10. (Exercise 28 in Probability Distributions) Let T be the random variable giving the
lifetime (in hours) of the graphics card in your computer. The manufacturer claims that T
has an exponential distribution with parameter   5,000 hours. (i) What is the
probability that your card fails after less than 3,000 hours? (ii) What is the probability
that your card lasts for at least 5,000 hours? (iii) What is the probability that your card
lasts for exactly 5,000 hours? (This carefully about this!)
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11. (Exercise 34 in Probability Distributions) Let X be an exponential random variable,
whose p.d.f. has the form
expected value of X?
f X ( x)  0.25  e  0.25 x , for
x  0 . What is the
**12.** (Exercise 36 in Probability Distributions) (i) Compute Rm  Rrf for your
team’s stock option data. (ii) Convert your ratios to normalized observations of Rnorm .
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