Assume that Bernoulli trials are to be performed until a first success occurs. Denote by XX the number of trials thus performed and by pp the probability of a success occurring on any given trial. Next, XX more Bernoulli trials are performed.
Finally, let YY denote the number of observed successes in this second group of trials.
Show that
E(Y)=1 and Var(Y)=2(1-p).