Let x and y be the amounts of time (in minutes) that a particular commuter must

Question

Let x and y be the amounts of time (in minutes) that a particular commuter must wait for a train on two independently selected days. Define a new random variable w by w = x + 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 w pictured. (This curve is called a triangular distribution, for obvious reasons!) (a) Verify that the total area under the density curve is equal to 1. Area = 1/2 (0.05) = (b) What is the probability that w is less than 20? P(w

Explanation / Answer

A) area = 1/2 * 40 * 0.05 = 1

B) P(W < 20) = 1/2 * 20 * 0.05 = 0.5

C) P(W < 10) = 1/2 * 10 * 0.025 = 0.125

D) P(W > 30) = 1/2 * (40-30) * 0.025 = 0.125

E) P(W < 30) = 1 - P(W > 30) = 1 - 0.125 = 0.875

P(10 < W < 30) = P(W < 30) - P(W < 10)

= 0.875 - 0.125

= 0.75

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