4. A certain river floods every year. Suppose that the low-water mark is set at 1 and the high-water mark Y has distribution function: FY (y) = P(Y y) = 1 1 y 2 , 1 y < + (a) Verify that FY (y) is a cdf. (b) Find fY (y), the pdf of Y .

5. Assume that the customer arrivals to a bank ATM are two per minute. (a) What is the probability of no arrival in the next minute? (b) What is the probability of at least two arrivals in the next minute? (c) What is the probability of at most two arrivals in the next four minutes? (d) If there is a second ATM with the same arrival rate, which the probability of no arrival in any ATM in the next minute?