1.A lecturer of Statistics tries to arrive at his office between 7:20 and 7:30 each morning. Because of some events beyond his control, the actual arrival time is between 7:10 and 7:40 and is described by the probability density function (pdf)f(x) = - ( x - 40 ) /450 if 10 X 40; and 0 elsewhere ( i.e. for X < 10 or for X > 40), where X is the number of minutes after 7:00.

a)Verify that f(x) is a pdf.

b)Find the cdf, E(X) and V(X).

c)Find the probability that the lecturer arrives between 7:20 and 7:30 on a given morning.