CS 3333 Mathematical Foundations
Spring '12
| Homework 9 |
Assigned on: 4/18 |
Due: 4/30 |
Solve the following problems from the textbook [S3]. Show the complete work,
not just the final answers, which are given in the book.
Page 66: 2.39 (pmf and CDF), 2.40 (pmf and CDF), 2.43 (CDF), 2.46
Page 67: 2.54, 2.55
Pages 69-71: 2.81, 2.83, 2.94
Page 99: 3.43, 3.55a, 3.56, 3.57, 3.60a, 3.61, 3.62
Page 144: Binomial: 4.61, 4.63, 4.64, 4.67, 4.68
Normal: 4.72, 4.74, 4.76, 4.79, 4.82, 4.84, 4.85
Poisson: 4.90, 4.91, 4.92, 4.93
Additional problems from [KR]:
- (# 11, p.492 Rosen) Suppose a fair die is rolled until a 6 comes up or
the die is rolled 10 times. Let X be the RV for the number of times the die
is rolled. Give (a) pmf of X and (b) E(X).
- (#13, p. 496, Rosen) Suppose n, n>=3, play "odd person out" to decide
who will buy a round of refreshments. Each person flips a fair coin
simultaneously. If exactly one coin comes up different from the rest of the
n-1 coins, then the corresponding person buys refreshments for everyone.
Otherwise, the people flip the coins again and continue until exactly one
coin has a different outcome than the rest of the coins.
(a) What is the probability that the odd person out is decided in just one
coin flip?
(b) What is the probability that the odd person out is decided with the kth
flip?
(c) What is the expected number of flips needed to decide odd person out
with n people?
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