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Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y). y = 1, 2, 3. c. List the cumulative distribution function F(x). d. List the cumulative distribution function F(v). e. Find the conditional distribution of f(xy), P(X=1 | Y = 3). f. Find the conditional distribution of f(x), P(X=3 | Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). x f(x, y) 2 3 1 0.05 0.05 0.10 3 0.05 0.10 0.35 y 5 0.00 0.20 0.10

Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y). y = 1, 2, 3. c. List the cumulative distribution function F(x). d. List the cumulative distribution function F(v). e. Find the conditional distribution of f(xy), P(X=1 | Y = 3). f. Find the conditional distribution of f(x), P(X=3 | Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). x f(x, y) 2 3 1 0.05 0.05 0.10 3 0.05 0.10 0.35 y 5 0.00 0.20 0.10

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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1. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y), y = 1, 2, 3. c. List the cumulative distribution function F(x). d. List the cumulative distribution function F(y). e. Find the conditional distribution of f(xy), P(X=1 | Y = 3). f. Find the conditional distribution of f(x), P(X=3 | Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). x f(x, y) 2 3 0.05 0.05 0.10 0.05 0.10 0.35 Y 0.00 0.20 0.10 1 3 5
Transcribed Image Text:1. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y), y = 1, 2, 3. c. List the cumulative distribution function F(x). d. List the cumulative distribution function F(y). e. Find the conditional distribution of f(xy), P(X=1 | Y = 3). f. Find the conditional distribution of f(x), P(X=3 | Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). x f(x, y) 2 3 0.05 0.05 0.10 0.05 0.10 0.35 Y 0.00 0.20 0.10 1 3 5
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