In any year, the weather can inflict storm damage to a home. From year to year, the damage is random. Let Y denote the dollar value of damage in any given year. Suppose that in 40% of the years Y = $0, in 25% of the years Y = $3, 000, in 10% of the years Y = $6, 000, in 6% of the years Y = $9, 000, and in the remaining Y = $12, 000.

(a) Please use a table to describe the probability distribution and the cumulative probability distribution of the random variable Y.

(b) What is the probability that the dollar value of damage in any given year is less than or equal to $9, 000, but larger than or equal to $3, 000?

(c) What are the expected value, variance, and standard deviation of Y?