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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: I 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. List the cumulative distribution function F(y). b. Find the conditional distribution of f(xly), P(X=11Y = 3). c. Find the conditional distribution of fivlx), P(X=31 Y = 3). d. Determine if the random variables are statistically independent considering f(2, 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: I 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. List the cumulative distribution function F(y). b. Find the conditional distribution of f(xly), P(X=11Y = 3). c. Find the conditional distribution of fivlx), P(X=31 Y = 3). d. Determine if the random variables are statistically independent considering f(2, 1)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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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: I f(r.y) T 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. List the cumulative distribution function F(y). b. Find the conditional distribution of f(xly), P(X=11Y = 3). c. Find the conditional distribution of fivlx), P(X=31 Y = 3). d. Determine if the random variables are statistically independent considering f(2, 1)
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: I f(r.y) T 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. List the cumulative distribution function F(y). b. Find the conditional distribution of f(xly), P(X=11Y = 3). c. Find the conditional distribution of fivlx), P(X=31 Y = 3). d. Determine if the random variables are statistically independent considering f(2, 1)
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