Suppose the following random numbers (1, 34, 22, 78, 56, 98, 00, 82) were selected during a Monte Carlo simulation that was based on the chart below. What was the average demand per period for the simulation? What is the expected demand?
$0.11.152.43.154.2\begin{array} { | c | c | c | c | } \hline \text { Demand } & \text { Probability } & \begin{array} { c } \text { Cumulative } \\\text { Probability }\end{array} & \begin{array} { c } \text { Interval of Random } \\\text { Numbers }\end{array} \\\hline 0 & .1 & & \\\hline 1 & .15 & & \\\hline 2 & .4 & & \\\hline 3 & .15 & & \\\hline 4 & .2 & & \\\hline\end{array}$

Question

Suppose the following random numbers (1, 34, 22, 78, 56, 98, 00, 82) were selected during a Monte Carlo simulation that was based on the chart below. What was the average demand per period for the simulation? What is the expected demand?

0.11.152.43.154.2\begin{array} { | c | c | c | c | } \hline \text { Demand } & \text { Probability } & \begin{array} { c } \text { Cumulative } \\\text { Probability }\end{array} & \begin{array} { c } \text { Interval of Random } \\\text { Numbers }\end{array} \\\hline 0 & .1 & & \\\hline 1 & .15 & & \\\hline 2 & .4 & & \\\hline 3 & .15 & & \\\hline 4 & .2 & & \\\hline\end{array}

Black Shadow · Accepted Answer

Final Answer :   Demand   Probability   Cumulative   Probability   Interval of Random   Numbers  0 . 1 . 1 01 − 10 1 . 15 . 25 11 − 25 2 . 4 . 65 26 − 65 3 . 15 . 8 66 − 80 4 . 2 1 81 − 00 \begin{array} { | c | c | c | c | } \hline 	ext { Demand }  &  	ext { Probability }  &  \begin{array} { c } 	ext { Cumulative } \	ext { Probability }\end{array}  &  \begin{array} { c } 	ext { Interval of Random } \	ext { Numbers }\end{array} \\hline 0  &  .1  &  .1  &  01 - 10 \\hline 1  &  .15  &  .25  &  11 - 25 \\hline 2  &  .4  &  .65  &  26 - 65 \\hline 3  &  .15  &  .8  &  66 - 80 \\hline 4  &  .2  &  1  &  81 - 00 \\hline\end{array}  Demand  0 1 2 3 4 ​  Probability  .1 .15 .4 .15 .2 ​  Cumulative   Probability  ​ .1 .25 .65 .8 1 ​  Interval of Random   Numbers  ​ 01 − 10 11 − 25 26 − 65 66 − 80 81 − 00 ​ ​   Tires sold sum is given by 0 + 2 + 1 + 3 + 2 + 4 + 4 + 4 = 20 over 8 periods. Thus the average demand was 20/8 = 2.5 tires.The expected demand is simply the EV, or .1(0) + .15(1) + .4(2) + .15(3) + .2(4) = 2.2 tires per period.

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