Calculating joint pmf, conditional pmf, finding covariance
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1) suppose that you repeatedly toss a coin whoes probability of head is p. Let X denote the number of tosses needed to get the first head and Y denote the number of tosses needed to get the second toss.
a) Find the joint pmf of X and Y.
b) Find the conditional pmf of Y given X=x.
c) Are X and Y independent?
d) (Bonus) Find the covariance of X and Y.
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The solution calculates joint pmf, conditional pmf and finds covariance.
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