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An assembly line has 17 machines and the number of machines X which fails to work is modeled by the binomial distribution with parameter p > 0: P(X= k) = ·(17) p² (1- 17-k (px (12), fy|x (0.49 | 12)) = 0.0556,0.7363 ³, k = 0, 1, ..., 17. However, the parameter p can not be estimated exactly and turns out to be from a random variable Y which has a uniform distribution on the interval (0, 1). 1. Find the unconditioned PMF px of X and evaluate P(X = 12). Hint: n-k [² (7) p² (1 − p)*-* dp = --P) 1 (n+1) 2. Given X = k, find the conditional PDF fyx (y k) and evaluate fyx (0.49 | 12)).

An assembly line has 17 machines and the number of machines X which fails to work is modeled by the binomial distribution with parameter p > 0: P(X= k) = ·(17) p² (1- 17-k (px (12), fy|x (0.49 | 12)) = 0.0556,0.7363 ³, k = 0, 1, ..., 17. However, the parameter p can not be estimated exactly and turns out to be from a random variable Y which has a uniform distribution on the interval (0, 1). 1. Find the unconditioned PMF px of X and evaluate P(X = 12). Hint: n-k [² (7) p² (1 − p)*-* dp = --P) 1 (n+1) 2. Given X = k, find the conditional PDF fyx (y k) and evaluate fyx (0.49 | 12)).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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How were the correct answers of 0.0556 and 0.7363 attained?

An assembly line has 17 machines and the number of machines X which fails to work is modeled by the binomial distribution with parameter p > 0: P(X= k) = · (77) ₁¹(¹. 17-k k(1-p)* ", k = 0, 1, ..., 17. However, the parameter p can not be estimated exactly and turns out to be from a random variable Y which has a uniform distribution on the interval (0, 1). 1. Find the unconditioned PMF px of X and evaluate P(X = 12). Hint: (px (12), fy|x (0.49 | 12)) = 0.0556,0.7363 1 (n+1) 2. Given X = k, find the conditional PDF fyx (yk) and evaluate fyx (0.49 | 12)). (₁) p² (1 - p)" - dp = n-k
Transcribed Image Text:An assembly line has 17 machines and the number of machines X which fails to work is modeled by the binomial distribution with parameter p > 0: P(X= k) = · (77) ₁¹(¹. 17-k k(1-p)* ", k = 0, 1, ..., 17. However, the parameter p can not be estimated exactly and turns out to be from a random variable Y which has a uniform distribution on the interval (0, 1). 1. Find the unconditioned PMF px of X and evaluate P(X = 12). Hint: (px (12), fy|x (0.49 | 12)) = 0.0556,0.7363 1 (n+1) 2. Given X = k, find the conditional PDF fyx (yk) and evaluate fyx (0.49 | 12)). (₁) p² (1 - p)" - dp = n-k
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