Additional info for problem 328 Suppose the distribution of

Additional info for problem:

3.28. Suppose the distribution of the toll depends on whether the car is domestic or foreign as follows. The domestic cars pay $1.00 with probability 4 and $2.00 with probability .6, while the foreign cars pay $1.00 with probability .25 and $2.00 with probability .75. Now compute the mean and the variance of the total toll collected at the booth over a 1-hour period.

Solution

X:The toll collected from a booth from each car.

Y:The toll collected from a booth over a 1-hour period.

Y=40*60*X

E(X)=(1*0.4+2*0.6)*0.45+(1*0.25+2*0.75)*0.55 = 1.6825

E(Y)=E(40*60*X)=40*60*E(X)=4038

E(X²)=(1*0.4+4*0.6)*0.45+(1*0.25+4*0.75)*0.55 = 3.0475

E(Y²)=E(2400²X²)=2400²E(X²)=17553600

V(Y)=E(Y²)-{E(Y)}²=1248156

Thus, mean=4038

variance=124815