Question 3.1: Suppose an insurance company pays the amount of $1,000 for l......
Suppose an insurance company pays the amount of $1,000 for lost luggage on an airplane trip. From past experience, it is known that the company pays this amount in 1 out of 200 policies it sells. What premium should the company charge?
Define the r.v. ~X~ as follows: X = 0 if no loss occurs, which happens with probability 1−(1/200) = 0.995, and X = −1,000 with probability {\textstyle\frac{1}{200}}=0.005. Then the expected loss to the company is: E X=-1,00{{0}}\times0.005\,=-5 . Thus, the company must charge $5 to break even. To this, it will normally add a reasonable amount for administrative expenses and a profit.
Even in this simple example, but most certainly so in more complicated cases, it is convenient to present the values of a (discrete) r.v. and the corresponding probabilities in a tabular form as follows.
| x | 0 | -1,000 | Total |
| f(x) | \frac{199}{200} | {\frac{1}{200}} | 1 |