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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.
