A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly (the tosses are independent). Deﬁne...

A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly (the tosses are independent). Deﬁne (X = number of the toss on which the ﬁrst H appears, Y = number of the toss on which the second H appears. Clearly 1X<Y. (i) Are X and Y independent? Why or why not? (ii) What is the probability distribution of X? (iii) Find the probability distribution of Y . (iv) Let Z = Y X. Find the joint probability mass function

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