Question

Suppose that 5% of the time Todd attends a concert twice a month, 40% of the time he attends a concert once a month, and 55% of the time he doesn't attend a concert at all in a given month. What is the expected value for the number of times Todd attends a concert during a month?

Answer 1

The expected value for the number of times Todd attends a concert during a month is 0.5.

Explanation:

We have these following probabilities:

5% probability of attending a concert twice a month, which means that P(X = 2) = 0.05

40% probability of attending a concert once a month, which means that P(X = 1) = 0.4

55% probability of not attending a concert during the month, which means that P(X = 0) = 0.55

What is the expected value for the number of times Todd attends a concert during a month?

We multiply each value by its probability. So

`E(X) = 0.05*2 + 0.4*1 + 0.55*0 = 0.1 + 0.4 = 0.5`

The expected value for the number of times Todd attends a concert during a month is 0.5.