08Ma2bSol3

# 08Ma2bSol3 - MA2B HOMEWORK 3 SOLUTIONS Problem 1 3.1.10(a...

This preview shows pages 1–2. Sign up to view the full content.

MA2B, HOMEWORK 3 SOLUTIONS Problem 1: 3.1.10 (a) The random variable S n is binomially distributed with distribution Bin(n,p) because it is equal to the number of successes in n independent Bernoulli (p) trials. (b)The random variable T m is binomially distributed with distribution Bin(m,p) because it is equal to the number of successes in m independent Bernoulli (p) trials. (c) The random variable S n + T m is binomially distributed with distribution Bin(n+m,p) because it is equal to the number of successes in n+m independent Bernoulli (p) trials. (d) Let X i be the indicator function that there is a success on the i th trial. We know from the statement of the problem that the outcome of any particular trial is independent of the results of all the other trials, so that the random variables X 1 , ..., X n + m are independent. Now we can use two results about independent ran- dom variables that may be found in Pitman’s book on page 154. The first is that disjoint blocks of random variables are independent. Thus we can define two joint random variables Y and Z as follows: Y = ( X 1 , ..., X n ) Z = ( X n +1 , ..., X n + m ) and we are guaranteed that Y and Z are independent. Note that Y and Z are random variables whose values are binary vectors of length n and m respectively.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern