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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69f3bceb-f08e-48ad-949e-8791b0eafdb0%2F62c15a60-f8af-49ce-9258-19d6c40a9e16%2Fh1k68k7_processed.jpeg&w=3840&q=75)
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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