Question

Suppose that 5% of the time Henry goes to the movies twice a month, 30 % of the time he goes to the movies once a month, and 65 % of the time he doesn't go to themovies at all in a given month. What is the expected value for the number of times Henry goes to the movies during a month?(Expected value=“answer” times per month)

Answer 1

Considering that X is "the number of times that Henry goes to the movies in a month"

This variable has 3 possible outcomes

`X=\mleft\lbrace0,1,2\mright\rbrace`

You know that 5% of the time he goes to the movies twice a month, 30% of the time he goes to the movies once a month and 65%of the time he doesn't go to the movies at all during the given month.

These percentages correspond to the probability of each one of x possible outcomes.

You can make a table of probability distribution:

The expected value is equal to the sum of the product of each value of x by its corresponding probability:

`\begin{gathered} E(X)=\Sigma x_iP(x_i) \\ E(X)=0\cdot0.65+1\cdot0.30+2\cdot0.05 \\ E(X)=0+0.30+0.1 \\ E(X)=0.4 \end{gathered}`

He is expected to go to the movies 0.4 times per month.