1. Consider the p.d.f. for the random variable Y = total waiting time for two buses. 0

1. Consider thc p.d.f. for the random variable Y = total waiting time for two f(y) o elsewhere (a) Sketch the p.d.f. and explain using symmetry why E(Y) 5. (b) Find E(Y) and V(Y). (c) In addition to the mean and variance, wc can summarize a random variable Y with a percentile value. The pth percentile of Y is thc value of y so that P(Y y) p. i. Another way of summarizing the center of a distribution is the median 50th percentile or p 0.5. Find the median of Y and compare its value to the mean of ii. Another way of summarizing the variability of a distribution is the interquartile range, which is calculated as the 75th percentile (or p = 0.75) minus the 25th percentile (or p = 0.25). Find Lhe interquartile range of Y and compare its value to the standard deviation of Y.