Soln1 - 1 ISyE 6739 Test#2 Solutions Summer 2005 This test is open notes open books You have exactly 90 minutes Just do the best you can and good

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 ISyE 6739 — Test #2 Solutions Summer 2005 This test is open notes, open books. You have exactly 90 minutes . Just do the best you can, and good luck! 1. (30 points) Short Answer Questions. (a) Suppose X has p.d.f. f ( x ) = 5 x 4 , 0 x 1. Find E [2 X - 5]. ANSWER: 2 E [ X ] - 5 = - 10 / 3. (b) If X again has p.d.f. f ( x ) = 5 x 4 , 0 x 1, find Var (2 X - 5). ANSWER: 4 Var ( X ) = 0 . 0793. (c) Suppose X can equal 1 or 2, each with probability 1 / 2. Find E [ n( X )]. ANSWER: 1 2 n(2) = 0 . 347. (d) TRUE or FALSE? E [ X 2 ] ( E [ X ]) 2 . ANSWER: True. (e) Suppose X has m.g.f. M X ( t ) = 0 . 3 e t + 0 . 7. What’s the distribution of X ? ANSWER: Bern(0.3). (f) If X has m.g.f. 4 / (4 - t ), for t < 4, find the m.g.f. of 2 X - 1. ANSWER: 4 e - t / (4 - 2 t ), t < 2. (g) TRUE or FALSE? If Cov ( X,Y ) = 0, then X and Y are independent. ANSWER: False.
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 (h) Suppose that X and Y are independent Exponential( λ ) random variables. What is the m.g.f. of
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/06/2010 for the course ISYE 6739 taught by Professor Tricahuu during the Spring '10 term at San Jose State University .

Page1 / 5

Soln1 - 1 ISyE 6739 Test#2 Solutions Summer 2005 This test is open notes open books You have exactly 90 minutes Just do the best you can and good

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online