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roblem 3. Consider the following joint probability mass function of two random variables X = {c, d] and Y € {1,2,3}: PxY(2,3) 1 2 3 0.1 0.3 0.2 0.2 0.1 0.1 C d Here c and d are some real numbers. 1. Is this a valid joint pmf? Provide formal justification. Compute Pr(X= c). Compute Pr(Y = 3). 2. Compute the conditional pmf of Y given X = c, i.e., compute Pr(Y=y|X = c) = py|x (ylc), for y = 1,2,3. Comp the expected value of this conditional pmf. 3. Compute the conditional pmf of X given Y = 3, i.e., compute Pr(X = x|Y = 3) = pxy (x|3), for x = c, d. Comp the expected value of this conditional pmf.

roblem 3. Consider the following joint probability mass function of two random variables X = {c, d] and Y € {1,2,3}: PxY(2,3) 1 2 3 0.1 0.3 0.2 0.2 0.1 0.1 C d Here c and d are some real numbers. 1. Is this a valid joint pmf? Provide formal justification. Compute Pr(X= c). Compute Pr(Y = 3). 2. Compute the conditional pmf of Y given X = c, i.e., compute Pr(Y=y|X = c) = py|x (ylc), for y = 1,2,3. Comp the expected value of this conditional pmf. 3. Compute the conditional pmf of X given Y = 3, i.e., compute Pr(X = x|Y = 3) = pxy (x|3), for x = c, d. Comp the expected value of this conditional pmf.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 31CR
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Problem 3. Consider the following joint probability mass function of two random variables X E {c, d] and YE {1,2,3}: PxY(2,y) 3 1 2 0.1 0.3 0.2 0.2 0.1 0.1 C d Here c and d are some real numbers. 1. Is this a valid joint pmf? Provide formal justification. Compute Pr(X = c). Compute Pr(Y = 3). 2. Compute the conditional pmf of Y given X = c, i.e., compute Pr(Y=y|X = c) = pyx (y|c), for y = 1,2,3. Compute the expected value of this conditional pmf. 3. Compute the conditional pmf of X given Y = 3, i.e., compute Pr(X = x|Y = 3) = Pxy(x|3), for x = c, d. Compute the expected value of this conditional pmf.
Transcribed Image Text:Problem 3. Consider the following joint probability mass function of two random variables X E {c, d] and YE {1,2,3}: PxY(2,y) 3 1 2 0.1 0.3 0.2 0.2 0.1 0.1 C d Here c and d are some real numbers. 1. Is this a valid joint pmf? Provide formal justification. Compute Pr(X = c). Compute Pr(Y = 3). 2. Compute the conditional pmf of Y given X = c, i.e., compute Pr(Y=y|X = c) = pyx (y|c), for y = 1,2,3. Compute the expected value of this conditional pmf. 3. Compute the conditional pmf of X given Y = 3, i.e., compute Pr(X = x|Y = 3) = Pxy(x|3), for x = c, d. Compute the expected value of this conditional pmf.
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