EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 9, Problem 9.7PTE
A transition
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Q1. A group of five applicants for a pair of identical jobs consists of three men and two
women. The employer is to select two of the five applicants for the jobs. Let S
denote the set of all possible outcomes for the employer's selection. Let A denote
the subset of outcomes corresponding to the selection of two men and B the subset
corresponding to the selection of at least one woman. List the outcomes in A, B,
AUB, AN B, and An B. (Denote the different men and women by M₁, M2, M3
and W₁, W2, respectively.)
Q3 (8 points)
Q3. A survey classified a large number of adults according to whether they were diag-
nosed as needing eyeglasses to correct their reading vision and whether they use
eyeglasses when reading. The proportions falling into the four resulting categories
are given in the following table:
Use Eyeglasses for Reading
Needs glasses Yes
No
Yes
0.44
0.14
No
0.02
0.40
If a single adult is selected from the large group, find the probabilities of the events
defined below. The adult
(a) needs glasses.
(b) needs glasses but does not use them.
(c) uses glasses whether the glasses are needed or not.
4. (i) Let a discrete sample space be given by
N = {W1, W2, W3, W4},
and let a probability measure P on be given by
P(w1) = 0.2, P(w2) = 0.2, P(w3) = 0.5, P(wa) = 0.1.
Consider the random variables X1, X2 → R defined by
X₁(w1) = 1, X₁(w2) = 2,
X2(w1) = 2, X2 (w2) = 2,
Find the joint distribution of X1, X2.
(ii)
X1(W3) = 1, X₁(w4) = 1,
X2(W3) = 1, X2(w4) = 2.
[4 Marks]
Let Y, Z be random variables on a probability space (, F, P).
Let the random vector (Y, Z) take on values in the set [0, 1] x [0,2] and let the
joint distribution of Y, Z on [0, 1] x [0,2] be given by
1
dPy,z (y, z) ==(y²z+yz2) dy dz.
harks 12 Find the distribution Py of the random variable Y.
[8 Marks]
Chapter 9 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 9 - Customers arrive at a bank at a Poisson rate ....Ch. 9 - Cars cross a certain point in the highway in...Ch. 9 - Suppose that in Problem 9.2, AI is agile enough to...Ch. 9 - Suppose that 3 white and 3 black balls are...Ch. 9 - Consider Example 2a. If there is a 50-50 chance of...Ch. 9 - Compute the limiting probabilities for the model...Ch. 9 - A transition probability matrix is said to be...Ch. 9 - On any given day, Buffy is either cheerful (c),...Ch. 9 - Suppose that whether it rains tomorrow depends on...Ch. 9 - A certain person goes for a run each morning. When...
Ch. 9 - Prob. 9.11PTECh. 9 - Determine the entropy of the sum that is obtained...Ch. 9 - Prove that if X can take on any of n possible...Ch. 9 - A pair of fair dice is rolled....Ch. 9 - A coin having probability p=23 of coming up heads...Ch. 9 - Prob. 9.16PTECh. 9 - Show that for any discrete random variable X and...Ch. 9 - Prob. 9.18PTECh. 9 - Events occur according to a Poisson process with...Ch. 9 - Prob. 9.2STPECh. 9 - Prob. 9.3STPECh. 9 - Prob. 9.4STPECh. 9 - Prob. 9.5STPE
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