Reference no: EM13587177

A coin is flipped until heads occur twice. Define two random variables X and Y to be the trial numbers at which the first and the second heads are observed. Assume that at any trial, the probability that a head occurs is p is between (0, 1). Where probability of tail is q=1-p (1).

(1) Show that the joint probability is given by

P(X = m, Y = n) = ( p²q^n-2 , where m = 1, 2, . . . ; and n = 2, 3, . . . ,

0 , otherwise.)

(2) Calculate the marginal probability mass function for X and Y.

(3) Calculate the conditional probability that X = m, given Y = n (i.e., P(X =m | Y=n)