Let X1,X2,…X_1, X_2, \ldotsX1,X2,… be i.i.d. Bernoulli(p)(p)(p) and define N=min{n:Xn=1}N = \min\{n: X_n = 1\}N=min{n:Xn=1} (the first success time). What is E[N]E[N]E[N]?
1p\frac{1}{p}p1
11−p\frac{1}{1-p}1−p1
p1−p\frac{p}{1-p}1−pp
ppp