Write a MATLAB code that will generate a random variable whi

Write a MATLAB code that will generate a random variable, which can take only five possible integer values 10,11,12,13, and 14. Generate a sequence of outcomes of 100 random trials. Count how many times 10 and 14 are generated out of the 100 outcomes. How can you estimate the probability of 10 and 14 in this case? Repeat the experiment with a 1 000, 5000 and 10000 outcomes generated. Estimate the probabilities in each case. What do you notice?

Thank you for helping :)

Solution

The MATLAB code for the problem is,

clear all

clc

prompt = \'Enter the number of samples:\';

N = input(prompt);

count10=0; % initiate the count for number 10

count14=0; % initiate the count for number 14

for i=1:N

outcome= randi([10 14],N,1);

end

for i=1:N % to count 10 & 14

if outcome(i)==10 % if outcome is 10 count increase

count10=count10+1;

elseif outcome(i)==14 % if outcome is 14 count increase

count14=count14+1;

end

end

prob_10 = count10/N; % probablity of occurance of 10

prob_14 = count14/N; % probablity of occurance of 14

fprintf(\'10 is generated %d times & 14 is generated %d times \ \', count10, count14);

fprintf(\'Probablity of occurance of 10 is %d \ Probablity of occurance of 14 is %d \ \', prob_10, prob_14);

The results of the MATLAB code are,

Enter the number of samples:100

10 is generated 26 times & 14 is generated 24 times

Probablity of occurance of 10 is 2.600000e-01

Probablity of occurance of 14 is 2.400000e-01

Enter the number of samples:1000

10 is generated 194 times & 14 is generated 190 times

Probablity of occurance of 10 is 1.940000e-01

Probablity of occurance of 14 is 1.900000e-01

Enter the number of samples:5000

10 is generated 1000 times & 14 is generated 998 times

Probablity of occurance of 10 is 2.000000e-01

Probablity of occurance of 14 is 1.996000e-01

Enter the number of samples:10000

10 is generated 2060 times & 14 is generated 1927 times

Probablity of occurance of 10 is 2.060000e-01

Probablity of occurance of 14 is 1.927000e-01

By increasing number of outcomes generated, the probability value gets more precise. The time taken for the computation also increased.