The median of a continuous random variable having distribution function F(x) is that value m such that F(m) = 0.5. That is, a random variable is just as likely to be larger than its median as it is to be smaller. The mode of a continuous random variable having density f(x) is the value of x for which f(x) attains its maximum. For each of the following random variables, (i) state and graph the density function and then (ii) compute the median, mode and mean and show these values on the graph.
(a) W uniformly distributed over the interval [a,b]
(b) Y exponential with rate