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
