Clément Canonne @ccanonne.github.io · Apr 28 Remember the example of X~Poisson(λ)? Well, computing the MGF of X then is either a matter of one line of computation. (Or even one quick lookup to Wikipedia, by the way, Even faster!) And you only need to do it ONCE. In your life.
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But wait, I still need to differentiate that, right? I want the n-th derivative of this thing evaluated at 0. That doesn't seem "simple" or "enjoyable." Yeah, it's not. Thankfully, you don't need to! You don't actually want the n-th derivative, you see. You want it *at 0.* Enter Taylor expansions.