In Statistics, the discrete Geometric Distribution is used when we want to determine the probability until first success when considering a discrete random variable, say X. The following equations are very useful when considering the geometric distribution

P(X=x)=(1−p)x−1pP(X=x)=(1−p)x−1p

E(X)=1pE(X)=1p

P(X

P(X>x)=(1−p)xP(X>x)=(1−p)x

Answer and Explanation:

Since there are ten numbers, then the probability of success is

p=110p=110

From the formulas in the context, we can clearly see that

a)

P(X=3)=(1−110)2110=0.081P(X=3)=(1−110)2110=0.081

b)

P(X<3)=1−[1−110]4=0.3439P(X<3)=1−[1−110]4=0.3439

c)

P(X>100)=[1−110]100=2.66×10−5P(X>100)=[1−110]100=2.66×10−5

d)

E(X)=1110=10