Bernouli Distribution

MID-TERM ASSIGNMENT

Question :

1. If an experiment will either succeed (成功) or fail (失敗). The probability of success is 30%, therefore, that of failure is 70%. To record the result of experiment, let 1 represents the success, and 0 represents the failure. In fact, this is so-called Bernoulli distribution (伯努力分配). How to create a random scalar, who has 30% of probability to be 1, while 70% of probability to be 0? In practice, we can make a random uniform distribution scalar (denoted by y, 0

1. Please make a random matrix (size=100×50) consisting of independent Bernoulli distribution (for any element of the matrix, it can be either 1 or 0, according to the probability of 30% and 70%, respectively)

Answer :

Explanation :

Method 1

vs=rndu(100,50); //I want to create random uniform consist of 100 rows and 50 columns//

result=zeros(100,50); //I want to fill the random uniform with zeros of 100 rows and 50 columns//

for i(1,100,1); //i represent the row. I want the rows start with 1 end in 100 with 1 interval//

    for j(1,50,1); //j represent the column. I want the column start with 1 end in 50 with 1 interval//

       if vs[i,j]>0.3;//to make command for the content of random uniform that I made, if greater than 0.3 means fail represent by 0//

        result[i,j]=0;//the result of the command that was made. 0=fail//

       else;//for other result//

        result[i,j]=1;//other than the above command or less than 0.3 means success represent by 1//

       endif; //to close the command//

    endfor;//to close the command//

endfor;//to close the command//

result;//to pull out the result//

[pic 1]

Method 2

vs=rndu(100,50); //I want to create random uniform consist of 100 rows and 50 columns//

result=zeros(100,50); //I want to fill the random uniform with zeros of 100 rows and 50 columns//

for i(1,100,1); //i represent the row. I want the rows start with 1 end in 100 with 1 interval//

    for j(1,50,1); //j represent the column. I want the column start with 1 end in 50 with 1 interval//

       if vs[i,j]<0.3;//to make partition for the content of random uniform that I made, if less than 0.3 means success represent by 1//

        result[i,j]=1;//the result of the partition that was made. 1=success//

       else;//for other result//

        result[i,j]=0;//other than the above command or bigger than 0.3 means fail represent by 0//

       endif; //to close the command//

    endfor;//to close the command//