Assignment1

# Assignment1 - AMA527 Decision Analysis Assignment 1 Due 13 October 2010 during lecture 1(a[5 pts A continuous random variable is said to have a

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: AMA527: Decision Analysis Assignment 1 Due 13 October 2010 during lecture 1.(a)[5 pts] A continuous random variable is said to have a gamma distribution with parameters ( t,λ ), λ > 0, and t > 0 if its density function is given by f ( x ) = λe- λx ( λx ) t- 1 Γ( t ) x ≥ x < , where Γ( t ) = Z ∞ e- y y t- 1 dy. Suppose that W , the amount of moisture in the air on a given day, is a gamma random variable with parameters ( t,β ). Suppose also that given that W = w , the number of accidents during that day - call it N- has a Poisson distribution with mean w . Show that the conditional distribution of W given that N = n is the gamma distribution with parameters ( t + n,β + 1). (b)[5 pts] The joint density function of X and Y is given by f ( x,y ) = 1 y e- ( y + x y ) , x > ,y > . Find E ( X ), E ( Y ), and show that V ( X,Y ) = 1. (c)[5 pts] The joint density of X and Y is given by f ( x,y ) = e- x/y e- y y , < x < ∞ ; 0 < y < ∞ ....
View Full Document

## This note was uploaded on 10/12/2010 for the course AMA AMA527 taught by Professor Dr.sim during the Spring '10 term at New School.

### Page1 / 2

Assignment1 - AMA527 Decision Analysis Assignment 1 Due 13 October 2010 during lecture 1(a[5 pts A continuous random variable is said to have a

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

View Full Document
Ask a homework question - tutors are online