Suppose you play a game. The rule is simple. You draw a random number from Norma

Question

Suppose you play a game. The rule is simple.

You draw a random number from Normal distribution (mean=0 and standard deviation=10).

Then, if the random number is greater than 0, you get $11.

If the random number is less than or equal to 0, you loose $10.

For simplicity, let's say that you play this game 3 times. Also, let's assume that the result of the game turned out to be

+11 -10 and 11.

In this case, the average gain/loss can be computed as (11-10+11)/3 = $4.00

Use R simulaiton to help.

Following the same procedure, what would be the average gain/loss if you played this game for 1,000,000 times?

Explanation / Answer

%%% Matlab R code %%%

clc;
clear all;
close all;
format long
N=1000000;
sum=0;
for n=1:N
r= 10*randn(1);
if ( r>0)
sum=sum+11;
else
sum=sum-10;
end
  
end
sum=sum/N;
if sum >0
fprintf('Avarage gain = $%f ',sum)
else
fprintf('Avarage loss = $%f ',sum)
end

OUTPUT:

Avarage gain = $0.499433

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