The expected value of a random variable can be calculated by:
[tex]E\lbrack X]=\sum_{i\mathop{=}1}^nx_i\cdot Pr(X=x_i)[/tex]
Where Pr(X = x_i) is the associated probability for the value x_i. Using the values from the table, we calculate the expectation value for the money a newly recruited customer can generate:
[tex]\begin{gathered} E\lbrack X]=0.4\cdot0+0.1\cdot10+0.2\cdot40+0.3\cdot100 \\ \\ \Rightarrow E\lbrack X]=\$39 \end{gathered}[/tex]
A newly recruited customer can be expected to generate $39.
Since the recruitment costs $50, it is not worth attempting to recruit new customers.
