Stochastic

# A little more calculus gives ex 2 z b a x2 b a dx b3

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: t line of the answer is easy to see. Since P (X > 0) = 1, we have P (X x) = 0 for x 0. For x 0 we compute Zx x P (X x) = e y dy = e y 0 = 1 e x 0 In many situations we need to know the relationship between several random variables X1 , . . . , Xn . If the Xi are discrete random variables then this is easy, we simply give the probability function that speciﬁes the value of P (X1 = x1 , . . . , Xn = xn ) whenever this is positive. When the individual random variables have continuous distributions this is described by giving the joint density function which has the interpretation that Z Z P ((X1 , . . . , Xn ) 2 A) = · · · f (x1 , . . . , xn ) dx1 . . . dxn A By analogy with (A.9) we must require that f (x1 , . . . , xn ) Z Z · · · f (x1 , . . . , xn ) dx1 . . . dxn = 1 0 and Having introduced the joint distribution of n random variables, we will for simplicity restrict our attention for the rest of the section to n = 2. The ﬁrst question we will confront is: “Given the joint distribution of (X, Y ), how do we recover the distri...
View Full Document

## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

Ask a homework question - tutors are online