(adsbygoogle = window.adsbygoogle || []).push({}); Let X; Y be two random variables with the following joint distribution（in the attachment）:

(a) Compute p(X) and p(Y )

(b) Compute p(X|Y = 1)

(c) compute p(Y = 1|X = 1) using (a) and (b)

(d) Are X and Y statistically independent? Show all your working.

This is my answer, but I don't know whether it's correct

(a) joint probabilities:

p(X=1)= 0+1/8=1/8

p(X=2)= 3/4+1/8=7/8

so p(X)= 1/8+7/8=1

p(Y=1)= 0+3/4=3/4

p(Y=2)=1/8+1/8=1/4

so p(Y)=3/4+1/4=1

just like Millennial said, I also don't understand this question, because I think it doesn't make any sense.

(b) p(Y=1,X) = p(Y=1)p(X|Y=1)

so p(X|Y=1) = p(Y=1, X)/p(Y=1) =?/(3/4)

here I have a question, I don't know how to compute p(Y=1,X), and btw does p(Y=1,X) = p(X, Y=1)?

(c) because I can't actually compute (b), so just leave it behind for now.

(d) because p(X=1,Y=1) = 0 and it doesn't equal to p(X=1)p(Y=1) = 1/8,so they are not statistically independent.

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# Homework Help: A EASY QUESTION FOR probability probability A easy question for probability

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