Problem 1 For the three functions below, either find a number k such that the given function is a probability density function or explain why no such number exists. a) f (x ) = (kx - 1)(x - 2) for 0 S x - 2 otherwise b) f (x ) = Jre-kx for x 2 0 otherwise ") f ( . ) = 10 In kx for 1 S x = 2 otherwise Problem 2 Use integration to find the indicated probabilities. 3 if x 2 1 f(x) = 0 if x 2)