| Line 28: | Line 28: | ||
:<math>M_X(s)=E[e^{sX}] = \int e^{sx} f_{X}(x)dx</math> | :<math>M_X(s)=E[e^{sX}] = \int e^{sx} f_{X}(x)dx</math> | ||
: get an answer for <math>s < \lambda </math> | : get an answer for <math>s < \lambda </math> | ||
| + | : note that the integrating range of x starts from 0 | ||
=== Answer 2 === | === Answer 2 === | ||
Write it here. | Write it here. | ||
Revision as of 12:39, 26 March 2013
Contents
Practice Problem: Obtain the moment generating function for an exponential random variable
Let X be an exponential random variable. Recall that the pdf of an exponential random variable is given by
$ \ f_X(x)= \lambda e^{-\lambda x}, \text{ for }x\geq 0 . $
Obtain the moment generating function $ M_X(s) $ of X.
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
Hint:
- $ M_X(s)=E[e^{sX}] = \int e^{sx} f_{X}(x)dx $
- get an answer for $ s < \lambda $
- note that the integrating range of x starts from 0
Answer 2
Write it here.
Answer 3
Write it here.
