Problems in Probability

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Fall 2011 Strategic Practice 6: Section 2 (Moment Generating Functions MGFs) - Question 2
If X has MGF M(t), what is the MGF of -X? What is the MGF of a + bX, where a and b are constants?
Solution: E(e^(t(a+bX))) = E(e^(at+btX)) = (e^at)E(e^(btX)) = e^at(M(bt)).
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."
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