Problem 1: The joint probability distribution of two random variables X and Y is given in the following table 0. 1 3 fy(y) Y 2 1/12 1/12 1/12 1/12 3 1/12 1/6 1/12 4 1/12 1/12 1/6 fx(x) a) Find the marginal density of X and the marginal density of Y. (add them to the above table) b) Are X and Y independent? c) Compute the P{Y >1|X > 2}. d) Compute the expected yalue of X

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Problem 1:
The joint probability distribution of two random variables X and Y is given in the following table
1
3
fy(y)
Y
1/12 1/12
1/12 1/12
1/12 1/6 1/12
1/12 1/12
2
3
4
1/6
fx(x)
a) Find the marginal density of X and the marginal density of Y. (add them to the above table)
b) Are X and Y independent?
c) Compute the P{Y >1|X > 2}.
d) Compute the expected value of X.
e) Compute the probability that X is greater or equal to Y +1.
f) Compute the conditional probability distribution of X given Y = 3.
Transcribed Image Text:Problem 1: The joint probability distribution of two random variables X and Y is given in the following table 1 3 fy(y) Y 1/12 1/12 1/12 1/12 1/12 1/6 1/12 1/12 1/12 2 3 4 1/6 fx(x) a) Find the marginal density of X and the marginal density of Y. (add them to the above table) b) Are X and Y independent? c) Compute the P{Y >1|X > 2}. d) Compute the expected value of X. e) Compute the probability that X is greater or equal to Y +1. f) Compute the conditional probability distribution of X given Y = 3.
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