d.Find the average waiting time between any two consecutivephone calls.

e.Find the median waiting time until the firstphone call.

10.Suppose that a random variable X has a probability density function given by ? (?) = {??7?−𝑥4? > 00elsewherea.Find, by inspection,the value of ?that makes ?(?)a density function. [Hint: what is the distribution of X? What are the values of its parameters? What is the expression for ?in terms of the parameters??]

b.What are the mean and standard deviation of ??

c.Find the (exact) probability ?[4 ≤ ? ≤ 12].

d.Use Chebyshev’s inequality to find the interval that contains at least 75% of values of X.2?2

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11.You arrive at a bus stop at 10 o’clock, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30. => ?𝑋(?) =30for 10: 00 < ? < 10: 30a.What is the probability that you will have to wait longer than 10 minutes? ?[? > 10: 10] = 20 ∙1

b.If, at 10:15, the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

12.If a parachutist lands at a random point on a line between markers A and B, find the probability that she is closer to A than to B. Find the probability that her distance to A is more than three times her distance to B.