# HW - X 1 X 1 X 2(Name it 8 Let X 1 and X 2 have the joint...

This preview shows page 1. Sign up to view the full content.

APPM 4/5520 Problem Set One (Due Wednesday, August 31st) 1. Let X be a random variable with the binomial distribution with parameters n and p , (ie: X bin ( n, p )). Find the distribution of Y = n - X . (Name it!) 2. Let X unif (0 , 1). Find the distribution of Y = - ln X . (Name it!) 3. Let X exp(rate = λ ). Find the distribution of Y = e - X . (Name it!) 4. Let X unif (0 , 1). Find the distribution of Y = tan X . (Name it!) 5. Compute the mean of the Γ( α, β ) distribution by “integrating without integrating”. 6. Let X be a continuous random variable with pdf f and cdf F . Let U unif (0 , 1). Show that Y = F - 1 ( U ) has the same distribution as X . 7. Suppose that X 1 , X 2 iid exp ( rate =
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X 1 X 1 + X 2 . (Name it!) 8. Let X 1 and X 2 have the joint pdf f X 1 ,X 2 ( x 1 , x 2 ) = 2 e-x 1-x 2 I (0 ,x 2 ) ( x 1 ) I (0 , ∞ ) ( x 2 ) . (a) Find the marginal pdfs for X 1 and X 2 . (b) Suppose that Y 1 = 2 X 1 and Y 2 = X 2-X 1 . Show that Y 1 and Y 2 are independent. 9. Required for 5520 students only: Suppose that X is a continuous random variable with pdf f ( x ). Let Y = X 2 . (Note that this is not a one-to-one, invertible transformation.) Find an expression for the pdf of Y in terms of the pdf of X ....
View Full Document

• Fall '11
• Manuel
• Probability distribution, Probability theory, probability density function, Cumulative distribution function, Discrete probability distribution, iid X1 X1

{[ 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