# quiz8 - STA 4321/5325 Spring 2010 Quiz 8 April 9 Name There...

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

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.

Unformatted text preview: STA 4321/5325 - Spring 2010 Quiz 8 - April 9 Name: There are ﬁve problems in this quiz. Each problem has exactly one correct answer. Problem 1 Let f (x, y ) denote the joint probability density function of two continuous random variables X and Y , and fX (x) denote the marginal probability density function of X . Then it is always true that (a) fX (x) = ∞ −∞ f (x, y )dx (b) fX (x) = ∞ 0 f (x, y )dy (c) fX (x) = f (x, 0) (d) fX (x) = ∞ −∞ f (x, y )dy Problem 2 Let X and Y be two discrete random variables with the following joint probability mass function: X p(x, y ) 0 1 2 0 1/9 2/9 1/9 Y 1 2/9 2/9 0 2 1/9 0 0 Then, (a) P (X = 1) = 4 81 (b) P (X = 1) = 2 9 (c) P (X = 1) = 4 9 (d) P (X = 1) = 1 Problem 3 Let X and Y be two continuous random variables with joint probability density function f (x, y ), and marginal density functions fX (x) and fY (y ) respectively. Then X and Y are said to be independent if f (x, y ) = fX (x)fY (y ) for every x ∈ R, y ∈ R. This statement is (a) True (b) False 1 Problem 4 Let X and Y be continuous random variables taking positive values, with joint probability density function given by f (x, y ) = e−(x+y) for every x > 0, y > 0. It can be derived that the marginal probability density function of Y is given by fY (y ) = e−y for y > 0. Then, the conditional probability density function of X given Y = 7 is given by (a) fX |Y =7 (x) = e−7 for every x > 0 (b) fX |Y =7 (x) = e−(x+7) for every x > 0 (c) fX |Y =7 (x) = e−x for every x > 0 (d) fX |Y =7 (x) = e−(y+7) for every x > 0 Problem 5 Let X and Y be two independent Bernoulli random variables. Let P (X = 0) = 1 and P (Y = 0) = 3 . Then, (a) P (X = 0, Y = 1) = 4 9 (b) P (X = 0, Y = 1) = 2 9 (c) P (X = 0, Y = 1) = 3 9 (d) P (X = 0, Y = 1) = 1 9 2 1 3 ...
View Full Document

## This note was uploaded on 06/05/2011 for the course STA 4321 taught by Professor Staff during the Spring '08 term at University of Florida.

### Page1 / 2

quiz8 - STA 4321/5325 Spring 2010 Quiz 8 April 9 Name There...

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

View Full Document
Ask a homework question - tutors are online