Referring to the previous exercise, let x and y be waiting times on two independently selected days.

Question:

Referring to the previous exercise, let x and y be waiting times on two independently selected days. Define a new
random variable w by w = x 1 y, the sum of the two waiting times. The set of possible values for w is the interval from 0 to 40 ( because both x and y can range from 0 to 20). It can be shown that the density curve of w is as pictured ( this curve is called a triangular distribution, for obvious reasons!):

a. Shade the area under the density curve that corresponds to P( w > 35).
b. Put the following probabilities in order from smallest to largest: P( w 30)
Explain your reasoning.