Please review the mean vaules to answer part D of this question.The mean value of the Y variable was 1.519.The mean value of the 500 simulated obersevations was 2.92. What does this illustrate? 5.45 Queuing Simulation. Benny's Barber Shop in Cleveland hasfive chairs for waiting customers. The number of customers waitingis a random variable Y with the following probability distribution.y1345P(Y = y)0.4240.1610.1340.1110.0930.077a. Compute and interpret the mean of the random variable Y.b. In a large number of independent observations, how many cus-tomers will be waiting, on average?c. Use the technology of your choice to simulate 500 observationsof the number of customers waiting.d. Obtain the mean of the observations in part (c) and compareit to µy.e. What does part (d) illustrate?

a) From the given data Y P(Y=y) yP(Y=y) 0 0.424 0 1 0.161 0.161 2 0.134 0.268 3 0.111…

Answered: 15 Queuing Simulation. Benny's Barber…

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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Please review the mean vaules to answer part D of this question.

The mean value of the Y variable was 1.519.

The mean value of the 500 simulated obersevations was 2.92.

What does this illustrate?

5.45 Queuing Simulation. Benny's Barber Shop in Cleveland has
five chairs for waiting customers. The number of customers waiting
is a random variable Y with the following probability distribution.
y
1
3
4
5
P(Y = y)
0.424
0.161
0.134
0.111
0.093
0.077
a. Compute and interpret the mean of the random variable Y.
b. In a large number of independent observations, how many cus-
tomers will be waiting, on average?
c. Use the technology of your choice to simulate 500 observations
of the number of customers waiting.
d. Obtain the mean of the observations in part (c) and compare
it to µy.
e. What does part (d) illustrate?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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