Thread: Random Variables

In order to verify the accuracy of their financial accounts, companies use auditors on a regular basis to verify accounting entries. The company's employees make erroneous entries 2% of the time. Suppose that an auditor randomly checks five entries. Let Y be the number of errors detected by the auditor.

a) What are the possible values of the random variable Y?
b) Find the probability function for Y.
c) Find the probability distribution function for Y.

My answer:
a) Y = {0,1,2,3,4,5}.
b) y 0 1 2 3 4 5
p(y)

I am stuck on finding the probability function for Y. Do I use the formula C(6,y)(0.02)^y(0.98)^(n-y)? Find the combination of six possibilities chosen y at a time, then multiply that by (0.02) raised to the y power, then multiply that by 0.98 raised to the (n-y).

Originally Posted by lovesmath

In order to verify the accuracy of their financial accounts, companies use auditors on a regular basis to verify accounting entries. The company's employees make erroneous entries 2% of the time. Suppose that an auditor randomly checks five entries. Let Y be the number of errors detected by the auditor.

a) What are the possible values of the random variable Y?
b) Find the probability function for Y.
c) Find the probability distribution function for Y.

My answer:
a) Y = {0,1,2,3,4,5}.
b) y 0 1 2 3 4 5
p(y)

I am stuck on finding the probability function for Y. Do I use the formula C(6,y)(0.02)^y(0.98)^(n-y)? Find the combination of six possibilities chosen y at a time, then multiply that by (0.02) raised to the y power, then multiply that by 0.98 raised to the (n-y).

The number of errors would have a binomial distribution B(5,0.2)

CB

Why is the binomial distribution B(5, 0.2) instead of B(6, 0.2)? Does that mean part a should be Y = {1,2,3,4,5}? I thought there had to be an option of getting 0 errors.

Originally Posted by lovesmath

Why is the binomial distribution B(5, 0.2) instead of B(6, 0.2)? Does that mean part a should be Y = {1,2,3,4,5}? I thought there had to be an option of getting 0 errors.

5 is the number checked

Binomial distribution - Wikipedia, the free encyclopedia

CB