A bus passes by a certain street corner every morning around 9:00 a.m. Let X be the difference (in minutes) between the time instant at which the bus passes and 9:00 a.m. We suppose that X has approximately a N(µ = 0, | ?2 = 25) distribution. We consider two independent days. Let Xk be the value of the random variable X on the kth day, for k = 1, 2.
a) Calculate the probability P(X1 ? X2 > 15).
b) Find the joint density function fX1,X2(x1, x2).
c) Calculate (i) P(X1 = 2 | X1 > 1) and (ii) P(X1 < 2 | X1 = 1).