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.
 Spring '10
 DURRETT
 The Land

Click to edit the document details