Solve all parts a-f below. Show all work.

1a.) 3 red cars arrive to Cumberland Farms in average per 15 min. Find P(No red cars arrive to Cumberland farms during the next 15 min).

b.) Find P(Exactly 3 cars will arrive at Cumberland farms over the next hour).

c.) The expected number of red cars arriving to Cumberland farms over the next 20 min is:

d.) Find c such that the following function represents the density of a continuous random variable X.

f(x)=cx^n for x in [0,1], and 0 otherwise.

e.) For the above random variable X compute P(X>x).

f.) For the above random variable X compute E[X].