Question

Keeping rolling a 4-sided die until you see the first ACE(SPOT 1). Let X be the number of rolls resulting

1. Find P[X = 3]

2. Find P[X >= 3]

3. Find E[X]

4. Find V[X]

Answer 1

here this follows geometric distribution with parameter p=probability of ace =1/4 =0.25

1)

probability =

P(X=3)=

(1-0.25)3-1*0.25=

0.1406

2)

probability =

P(X>=3)=

1-P(X<=2)=

(1-0.25)3-1=

0.5625

3)

here mean of distribution=E(x)=1/p=

4.00

4)

varaince =σ2=(1-p)/p2=

12.00