How to get the E[x] and Var[x]? While several million cars drive on the Pennsylvania Turnpike over a holiday weekend, the number of passenger cars taking a specific exit off the Turnpike on Thanksgiving weekend averages $5$ per minute. Of those $50$% have only the driver; $30$% have $2$ people in the car; $10$% have three people and $5$% have $4$ people; and $5$% have $5$ people. Let X = the total number of people that are in the cars passing through a tollbooth at this exit in the next $10$ minutes. Find E(X) and Var(X). How to solve this problem? I don't have any clue about it.

Total number of cars passing in 10 minutes is $10 \times 5 = 50.$ Hence,

\begin{align} \mathbb{E}[X] & = 50 \times \left[\left( 1 \times \dfrac{50}{100} \right) + \left(2 \times \dfrac{30}{100} \right) + \left(3 \times \dfrac{10}{100}\right) + \left(4 \times \dfrac{5}{100} \right) + \left( 5 \times \dfrac{5}{100}\right)\right] \\\ & = 50 \times (0.5 + 0.6 + 0.3 + 0.2 + 0.25) = 92.5 \end{align}