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  3. consider the two dependent discrete random variabl

Consider the two dependent discrete random variables X and Y . The variable X takes values in...

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Statistics

Consider the two dependent discrete random variables X and Y .The
variable X takes values in {−1, 1} while Y takes values in {1, 2,3}. We observe that

P(Y =1|X=−1)=1/6
P(Y =2|X=−1)=1/2
P(Y =1|X=1)=1/2
P(Y =2|X=1)=1/4
P(X = 1) = 2/ 5
(a) Find the marginal probability mass function (pmf) of Y .
(b) Sketch the cumulative distribution function (cdf) of Y .
(c) Compute the expected value E(Y ) of Y .
(d) Compute the conditional expectation E[Y |X = 1].

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