{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# assn7 - Math 361 Problem set 7 Due 1(1.9.6 Let the random...

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

Math 361, Problem set 7 Due 10/25/10 1. (1.9.6) Let the random variable X have E [ X ] = μ , E [( X - μ ) 2 ] = σ 2 and mgf M ( t ), - h < t < h . Show that E X - μ σ = 0 , E " X - μ σ 2 # = 1 and E exp t X - μ σ = e - μt/σ M t σ , - hσ < t < hσ. (Recall: exp( x ) = e x ). 2. (1.9.7) Show that the moment generating function of the random variable X having pdf f ( x ) = 1 3 for - 1 < x < 2, zero elsewhere is M ( t ) = e 2 t - e - t 3 t t 6 = 0 1 t = 0 3. (1.9.18) Find the moments of the distribution that has mfg M ( t ) = (1 - t ) - 3 , t < 1. Hint: Find the MacLaurin’s series for M ( t ). 4. (1.9.23) Consider k continuous-type distributions with the following char- acteristics: pdf f i ( x ), mean μ i and variance σ 2 i , i = 1 , 2 , . . . , k . If c i 0, i = 1 , . . . , k and c 1 + · · · + c k = 1, show that the mean and variance of the distribution having pdf

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