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Conditional Expectation Example

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Suppose you are interested in determining the conditional expected value of the number of customers at your doughnut shop after you post 20 advertisements of your shop around your town.

From previous experiences, you've calculated the conditional probabilities of observing customer numbers ($C$) after posting 20 advertisements ($ad$) to be:

$$Pr(C=50|ad=20)=0.24$$
$$Pr(C=60|ad=20)=0.08$$
$$Pr(C=75|ad=20)=0.03$$

What is the conditional expectation of customers?

A

19

B

54

C

40

D

62

E

48