A fair coin is tossed three times. Let X denote a random variable that takes the value 0 if the first toss is a head and the value 1 if the first toss is a tail. Let Y be a random variable that defines the total number of heads in the three tosses. Find the joint pmf of X and Y. Prove that X and Y are not independent.
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What have you tried and where are you having trouble? – Graham Kemp Oct 05 '21 at 04:00
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im not sure how to solve this – user976242 Oct 05 '21 at 04:04
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Well, $\mathsf P(X=0, Y=1)=\tfrac 1{2^3}$ , being the probability that the first coin is a head and only one coin is a head. – Graham Kemp Oct 05 '21 at 04:12