tour planner insurance?

Yes you are correct your expectation is the average of the premiums. This should not be confused with the variance of a random variable or distribution which is the expectation or mean of the squared deviation of that variable from its expected value or mean. The third and fourth moments of the probability generating function are referred to somewhat amusingly as kurtosis and weight in the tails. That's usually enough oomph to select a function to sufficiently describe the population.

Please post these types of questions in the appropriate forum in future.