Question

Decision analysis. After careful testing and​ analysis, an oil company is considering drilling in two different sites. It is estimated that site A will net ​$20 million if successful​ (probability.2) and lose ​$4 million if not​ (probability.8​);site B will net ​$60 million if successful​ (probability.1) and lose ​$5 million if not​ (probability.9​). Which site should the company choose according to the expected return from each​ site?

Answer 1

Answer:

Given that:

Decision analysis,After careful testing and analyisis company is considering drilling in two different sites.

If the probability distribution for the random variable X,

xi x1 x2........xn

pi   p1 p2.......pn

Where pi =p(xi) ,we defind the expected value of X,denoted E(X),by the formula

Let X1 be the random variable foe site A.

Now we from the probability for X1 ,that is the payoff table and compute the expected value.

payoff table

xi	$20	-$4
pi	.2	.8

Thus the expected value can be calculated as,

E(X)=20(.2)-4(.8)

E(X)=4-3.2

E(X)=0.8

Let X2 be the random variable foe site B.

Now we from the probability for X2,that is the payoff table and compute the expected value.

payoff table

xi	$60	-$5
pi	.1	.9

Thus the expected value can be calculated as,

E(X)=60(.1)-5(.9)

E(X)=6-4.5

E(X)=1.5

Therefore,according to the expected return site B should be choose that is $1.5 millions.