# Random Variables

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• Oct 3rd 2011, 12:23 PM
lovesmath
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).
• Oct 3rd 2011, 12:31 PM
CaptainBlack
Re: Random Variables
Quote:

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
• Oct 3rd 2011, 12:49 PM
lovesmath
Re: Random Variables
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.
• Oct 3rd 2011, 01:18 PM
CaptainBlack
Re: Random Variables
Quote:

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