a) Find k such that the function is a probability density function over the given interval. b) Then write the probability density function. ƒ(x) = [5, 20] k -, X

(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1,2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0.

Find the value of k that makes the given function a probability density function on the specified interval. f(x) = kx 2 ≤ x ≤ 6 k= || =

Solve using R. Show all work.