Problem 3. A geological study indicates that an exploratory oil well drilled in

Question

Problem 3.

A geological study indicates that an exploratory oil well drilled in a certain region should strike oil with probability 0.25. Suppose a drilling company randomly keeps drilling wells until they strike oil. Let x=Number of dry wells dug when the first strike of oil

a. ProvideP(X= 5)

(1 pt)

b. Provide

E(2X+ 10) and V(2X+ 10)

(1 pt)

c. ProvideE[(X+ 3)^2]

.

(1 pt)

d. ProvideP(X >3|X >2)

.

(1 pt)

e. Provide an interval such that the probability thatXlies in the interval is at least 99%

.

(1 pt)

Explanation / Answer

a) here this is geometric distribution with p=0.25

P(X=5) =P(first four drills failure and 5th success) =(1-0.25)4*0.25 =0.0791

b)

E(2X+10) =2E(X)+10 =2*(1/p) +10 =2*(1/0.25)+10 =18

V(2X+10) =4*V(X) =4*(1-p)/p2 =4*(1-0.25)/'0.252 =48

c) E((X+3)2) = E(X2+9+6X) =E(X2) +9+6E(X) =(2-p)/p2+9+6*1/p =(2-0.25)/0.252 +9+6/0.25 =28+9+24 =61

d)

P(X>3|X>2) =P(X>3)/P(X>2) =(0.75)3/(0.75)2 =0.75

e) P(X<x) >0.99

P(X>x) <0.01

(1-0.25)x <0.01

taking log and solving

x >=16.007

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