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)
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...
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1467f162-7185-45ab-925a-2589d3c8cce7%2F55d37b86-3f37-4e0a-8598-77d1c5c56591%2Fm9enecv_processed.png&w=3840&q=75)
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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)