The number of claims in a calendar year for an insured has a probability function indicated below.
When a claim occurs, the claim amount , regardless of how many claims the insured will have in the calendar year, has probabilities and . The claim amounts in a calendar year for this insured are independent.
Let be the total claim amount for this insured in a calendar year. Calculate .
A bowl has 3 red balls and 6 white balls. Select two balls at random from this bowl with replacement. Let be the number of red balls found in the two selected balls. When where , roll a fair die times.
Let be the sum of the rolls of the die. Calculate .