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. Assume that x and y have a uniform distribution. 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 pictured. (This curve is called a triangular distribution, for obvious reasons!) Density 0.05
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. Assume that x and y have a uniform distribution. 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 pictured. (This curve is called a triangular distribution, for obvious reasons!) Density 0.05
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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7.3.4
Transcribed Image Text: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. Assume that x and y have a uniform distribution. 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 pictured. (This curve is called a triangular
distribution, for obvious reasons!)
Density
0.05
0
Area =
20
1
2
(a) Verify that the total area under the density curve is equal to 1. (Hint: The area of a triangle is
1
(base) (height).)
2
)(0.05)
=
(b) What is the probability that w is less than 20?
P(w < 20) =
40
(c) What is the probability that w is less than 10?
P(w < 10) =
W
Minutes
(d) What is the probability that w is greater than 30?
P(w > 30) =
(e) What is the probability that w is between 10 and 30? (Hint: It might be easier first to find the probability that w
is not between 10 and 30.)
P(10 < W< 30) =
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