Homework Help is Here – Start Your Trial Now!
Math
Probability
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(xly), P(X= 11Y = 3). f. Find the conditional distribution of f (ylx), P(X=31 Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). x f(x,y) 1 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(y). e. Find the conditional distribution of f(xly), P(X= 11Y = 3). f. Find the conditional distribution of f (ylx), P(X=31 Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). x f(x,y) 1 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...
See similar textbooks
icon
Related questions
Question
100%
Questions d, e and f
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(xly), P(X=1| Y = 3). f. Find the conditional distribution of f (ylx), P(X = 31 Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). I f(x,y) 1 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: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(xly), P(X=1| Y = 3). f. Find the conditional distribution of f (ylx), P(X = 31 Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). I f(x,y) 1 2 3 0.05 0.05 0.10 0.05 0.10 0.35 Y 0.00 0.20 0.10 1 3 5
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer