EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
Author: Ross
Publisher: VST
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Chapter 9, Problem 9.10PTE
A certain person goes for a run each morning. When he leaves his house for his run, he is equally likely to go out either the front or the back door, and similarly, when he returns, he is equally likely to go to either the front or the back door. The runner owns 5 pairs of running shoes, which he takes off after the run at whichever door he happens to be. If there are no shoes at the door from which he leaves to go running, he runs barefooted. We are interested in determining the proportion of time that he runs barefooted.
a. Set this problem up as a Markov chain. Give the states and the transition
b. Determine the proportion of days that he runs barefooted.
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Please plot graphs to represent the functions
EXAMPLE 6.2
In Example 5.4, we considered the random variables Y₁ (the proportional amount
of gasoline stocked at the beginning of a week) and Y2 (the proportional amount of
gasoline sold during the week). The joint density function of Y₁ and Y2 is given by
3y1, 0 ≤ y2 yı≤ 1,
f(y1, y2) =
0,
elsewhere.
Find the probability density function for U = Y₁ - Y₂, the proportional amount of
gasoline remaining at the end of the week. Use the density function of U to find E(U).
7.20
a
If U has a x² distribution with v df, find E(U) and V (U).
b Using the results of Theorem 7.3, find E(S2) and V (S2) when Y₁, Y2,..., Y, is a random
sample from a normal distribution with mean μ and variance o².
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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