Moment generating function

  • Thread starter Despondent
  • Start date
  • #1
Despondent
13
0

Homework Statement



Use conditional expectation to compute the moment generating function M_z(s) of the random variable Z=XT.


Homework Equations



X ~ R(0,10)
T ~ exp(0.1)

The Attempt at a Solution



By definition:

M_z(s) = E(exp(sZ))
=E(exp(sXT))

The only thing I can think of doing is using double expectation.

So M_z(s) = E[E(exp(sXT|X)] = E[E(exp(sXT|T)]...(1)

But here I'm stuck. Both X and T are continuous random variables so I can't just plug in the values of X and T one by one. Writing (1) as an integral of an expectation doesn't help either because I don't have an expression for the integrand and so cannot evaluate the integral. This question is really doing me in and any help to relieve my great pain would be much appreciated.
 

Answers and Replies

Suggested for: Moment generating function

Replies
3
Views
198
  • Last Post
Replies
4
Views
784
  • Last Post
Replies
4
Views
904
Replies
1
Views
803
Replies
13
Views
911
  • Last Post
Replies
3
Views
498
  • Last Post
Replies
12
Views
609
Replies
2
Views
109
Replies
8
Views
121
Top