Stat 330 (Spring 2015): Homework 5
Due: February 23, 2015
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and one additional
randomly chosen problem will be graded. Show all work for full credit.
1. * Suppose that the average number of log-ins to a Statistics department server is 6 per minute. What is
the probability that
a) no log-ins in a 1-minute period?
b) one or two log-ins in a 1-minute period?
c) more than 25 log-ins in a 5-minute period?
2. A central database server receives, on the average, 25 requests per second from its clients. What is the
probability that the server will receive
(a) no requests in a 10-millisecond interval?
(b) more than 2 requests in a 10-millisecond interval?
3. * The joint pmf of two discrete r.v. X and Y is given as:
X\Y
−2
−1
1
2
−1
1/16
1/8
1/8
1/16
0
1
1/16 1/16
1/16 1/8
1/16 1/8
1/16 1/16
(a) Find the marginal pmf’s of X and Y , respectively.
(b) Find the following probabilities:
i. P (X ≥ 2)
ii. P (X > Y )
iii. P (Y > 0)
(c) Are X and Y independent?
(d) Are X and Y uncorrelated?
(e) Calculate E[W ] and V ar[W ] where W = 2X − 3Y .
4. (Baron’s book): 3.24
5. (Baron’s book): 3.31
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