Considering that X is "the number of times that Henry goes to the movies in a month"
This variable has 3 possible outcomes
[tex]X=\mleft\lbrace0,1,2\mright\rbrace[/tex]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:
[tex]\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}[/tex]He is expected to go to the movies 0.4 times per month.
