First Midterm 2007

First Midterm 2007 - Examination I October 1 2006 I Given f...

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

View Full Document Right Arrow Icon
Examination I October 1, 2006 I. Given   , f x y such that   22 5 7 1 3 1 1 , 24 24 6 8 24 6 f x y x x y xy y Defined over   , 0,2 xy . A. Is this a valid probability density function? (10 Points) B. Derive the marginal distribution of y . (10 Points) C. Derive the conditional distribution of x given y . (10 Points) D. Are x and y independent? (10 Points). II. Given that x is distributed   0,8 U and that 1 3 yx A. What are the conditions for deriving   gy (the probability density function for y ) based on   ? (10 Points) B. Derive the distribution   . (10 Points). III. Assume   2 9 y fy where   0,3 y . A. Derive the moment generating function for y . (10 Points) B. Compute the first three moments for this distribution. (10 Points) C. Using the random variables in Table 1, calculate the first three sample moments. Do you think that these random variables are from   ? (10 Points) IV. Given 1 2 4 2 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

Page1 / 2

First Midterm 2007 - Examination I October 1 2006 I Given f...

This preview shows document pages 1 - 2. Sign up to view the full document.

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