Mathematics for Business Decisions, Part II
Homework 7
for
Math 115b, Section:
Instructor: James Barrett
Date:
by
Team:
We, the undersigned, maintain that each of us participated fully and equally in the completion of
this assignment and that the work contained herein is original. Furthermore, we acknowledge
that sanctions will be imposed jointly if any part of this work is found to violate the Student
Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for
this course.
_ Name Typed
Signature
% of Grade
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1. Let X be a random variable whose p.m.f. is given below.
x
1
f X (x)
0.2
0
0.4
1
0.2
2
0.1
4
0.1
Use Excel to compute V (X ) and  X . Show complete table.
Solution:
2. Let X be a finite random variable which can assume only the values 1, 2, 5, 10,
and 100. (i) μ X  (ii) If each of these values is equally likely to occur use
Excel to compute V (X ) and  X . Give your answers rounded to two decimal
places. Show table.
Solution:
3. 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.
Solution:
4. Let X be a binomial random variable with n  20 and p  0.75 . 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.
Solution:
5. Let W be the working lifetime, measured in years, of the microchip in your new
digital watch. The manufacturer claims that W has an exponential distribution with
a mean lifetime of 5 years. Use Excel and the method of Example 4 to compute
the variance and standard deviation of W. Verify using the short cut.
Solution.
6. Let X be the time, measured in hours and fractions of hours, from the start of
daily trading on the New York Stock Exchange until the Dow Jones Industrial
Average attains its maximum value for the given day. Assuming that X is a
continuous uniform random variable on [0, 7] , compute the variance and standard
deviation of X.
Solution:
7. Let X be the continuous random variable with p.d.f.
1.5  x  0.75  x 2
f X ( x)  
0
if 0  x  2
elsewhere
,
Use Integrating.xlsm to compute μx, V (X ) and  X .
Solution:
8. 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) .
Verify with short cut.
Solution:
9. 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
Show table
Solution:
10. Use VAR and STDEV to compute s 2 and s for the sample in Problem 9.
Solution:
11. Let X be a random variable with a mean of 8.2 and a standard deviation of
0.79. Let x be the sample mean for random samples of size n  150 . Compute the
expected value, variance, and standard deviation of x .
Solution:
12. Let R be the random variable which 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. See Auction Focus.xlsx for work on class
project.
Solution: