Expected Value Question 5

The number of tickets purchased by a computer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer.

\begin{array}{|r|c|c|c|c|c|} \hline \text{Number of tickets purchased} & 1 & 2 & 3 & 4 & 5 \\ \hline \text{Relative frequency} & 0.20 & 0.45 & 0.10 & 0.20 & 0.05 \\ \hline \end{array}

Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?

$2.45

$24.50

$29.40

$36.00

Approach

For discrete random variable $X$ :

\mu_x = E(X) = \sum x_iP(x_i)

= 1(0.20)+2(0.45)+3(0.10)+4(0.20)+5(0.05)

= 2.45

So the expected number of tickets purchased is 2.45. At $12 a piece:

2.45(12) = \boxed{29.40}