A LAW FIRM TAAKES CASES ON A CONTIGENT FEE BASIS IF THE CASE

A LAW FIRM TAAKES CASES ON A CONTIGENT FEE BASIS .IF THE CASE GOES TO TRAIL ,THE FIRM EXPECTS TO EARN $25000 AS PART OF THE SETTLEMENT IF IT WINS AND NOTHING IF IT DOES NOT.THE FIRM WINS ONE-THIRD OF THE CASES THAT GO TO TRAIL.IF THE CASE DO NOT GO TO TRAIL.HALF OF THE CASE DO NOT GO TO TRAIL.BE SURE YOU ADD APPROPRITE UNIT.

DEFINE A RANDOM VARIBALE TP MODEL THE EARNING OF TAKING A CASE OF THIS TYPE.

WHAT IS THE EXPECTED VALUE OF SUCH FIRM

WHAT IS THE STANDARD DEVIATION OF THE EARNING

Solution

Let X be the earning of the case

X can take 3 possibilities

i) Goes to trial -- 1/2 --wins -- 1/3 -- 25000

                                 -- does not win -- 2/3 ---000

ii) Does not go to trial -- 1/2 --00

Thus X can take values as 25000 or 0

Prob (X=25000) = 1/2(1/3) =1/6

Prob (x=0) = 5/6

Expected value of X = 1/6(25000) = 4166.67 dollars

E(X^2) = 1/6 (25000)^2

Var (x) = 86805527.78

std dev (x) = 9316.95