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Business Mathematics II
Homework 8
for
Math 115b, Sections: 18
Instructor: Ratnayaka
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Problem 1
Use Variance.xls to compute 10 samples, each of size n  3 , for both X and Y. (i) Compute the
average of the 10 sample errors for the samples from X and (ii) do the same for the 10 sample
errors for the samples from Y.
Problem 2
Let X be a random variable whose p.m.f. is given below.
x
f X (x)
1
0.2
0
0.4
1
0.2
2
0.1
4
0.1
Use Excel to compute V ( X ) and  X .
Problem 3
Let X be a finite random variable, which can assume only the values 1, 2, 5, 10, and 100. If each
of these values is equally likely to occur use Excel or a calculator to compute V ( X ) and  X .
Problem 4
Let X be a binomial random variable with n  6 and p  0.3 . In an Excel file, create a table
that lists the possible values of X, and use BINOMDIST to list the probabilities of these values.
(See Finite Random Variables in Distributions for a discussion of BINOMDIST.) Use the
method of Example 2 and an Excel file that is similar to Binomial 2.xls to compute the variance
and standard deviation of X.
Problem 5
Let X be a binomial random variable with n  6 and p  0.3 . Use the special formulas for
mean and variance that apply only to binomial random variables, to compute the mean, variance,
and standard deviation of X.
Problem 6
Let W be the working lifetime (in years) of the microchip in your new digital watch. The
manufacturer claims that W has an exponential distribution with mean lifetime of 5 years. Use
Excel and the method of Example 4 to compute the variance and standard deviation of W.
Problem 7
Let X be the continuous uniform random variable on [0,10] . Compute the mean, variance, and
standard deviation of X.
Problem 8
Let X be the continuous random variable with p.d.f.
if x  0
0
f X ( x)  
2
2x3
if 0  x.
6  x  e
Use Integrating.xls to compute V ( X ) and  X .
Problem 9
Let X be the continuous random variable that is uniform on [0,8] , and let S be the standardization
of X. Use the method of Example 7 to compute P (1  S  1) .
Problem 10
Let X be the exponential random variable with parameter   3 . Recall that both the mean and
standard deviation of X are equal to three. Let S be the standardization of X. Compute P ( S  1) .
First express P ( S  1) in terms of a probability for X, then use the formula for the cumulative
distribution function of X to finish the exercise. See Continuous Random Variables in
Distributions.)
Problem 11
Use Excel and the method of Example 8 to compute the mean, variance, and standard deviation
of the following random sample for the values of a random variable X.
10.2, 6.2, 10.8, 10.2, 12.1, 7.7, 10.7, 6.4, 13.1
Problem 12
Use VAR and STDEV to compute s 2 and s for the sample in Exercise 17.
Problem 13
Let X be a random variable with a mean of 75 and a standard deviation of 6. Let x be the
sample mean for random samples of size n  20 . Compute the expected value, variance, and
standard deviation of x .
* Problem 14
* Let R be the random variable that gives the error in a signal from your team’s data. Compute
your sample standard deviation, s, as an assumed value for the standard deviation,  R , of R.