A movie theater sells three kinds of tickets – children (for$3), adult (for $8),

Question

A movie theater sells three kinds of tickets – children (for$3), adult (for $8), and seniors (for $5). The number of childrentickets has E[C]=45 and V[C]=100. The number of adult tickets hasE[A]=137 and V[A]=610. Finally, the number of senior tickets hasE[S]=34 and V[S]=90. You may assume the number of tickets in eachgroup is independent. Any particular movie costs $300 to show,regardless of the audience size.

a. Write a formula relating C, A, and S to the theater’sprofit P for a particular movie.
b. Compute E[P] and V[P].

Explanation / Answer

Let P be profit. For anygiven showing P=3C+8A+5S-300 The expected profit is givenby E(P)=3E(C)+8E(A)+5E(S)-300 E(P)=3(45)+8(137)+5(34)-300=$1102 Using the relation thatV(aX)=a2V(X) we have

V(P)=9V(C)+64V(A)+25V(S) V(P)=9(100)+64(610)+25(90)=$42,190

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