It is known that 15% of US home mortgages are under water (i.e. the homeowner owesmore than the house is worth). Suppose 18 mortgages are randomly selected (assume independence). Let the random variable X equal the number that are under water.

(a) What is the distribution of X? Be sure to state all parameters.

(b) Find the probability that exactly 3 are under water.

(c) Find the probability that 1 or more are under water.

(d) Given that 1 or more are under water, determine the probability that 2 or more

are underwater.

(e) On average, how many do we expect to be under water?

(f) Find V ar(X)