![probability - Computing the moment-generating function of $f(x)=e^{-x}$ - Mathematics Stack Exchange probability - Computing the moment-generating function of $f(x)=e^{-x}$ - Mathematics Stack Exchange](https://i.stack.imgur.com/po2Y5.png)
probability - Computing the moment-generating function of $f(x)=e^{-x}$ - Mathematics Stack Exchange
![Generating Function | Hermite Generating function | Hermite poly. Generating function Based Question - YouTube Generating Function | Hermite Generating function | Hermite poly. Generating function Based Question - YouTube](https://i.ytimg.com/vi/UDXahQncdYw/maxresdefault.jpg)
Generating Function | Hermite Generating function | Hermite poly. Generating function Based Question - YouTube
![SOLVED: a) Suppose a random variable X has the moment generating function MX(t) := E[e tX]. Let g(t) := log MX(t), then prove that g 00(0) = Var[X]. (b) Suppose a random SOLVED: a) Suppose a random variable X has the moment generating function MX(t) := E[e tX]. Let g(t) := log MX(t), then prove that g 00(0) = Var[X]. (b) Suppose a random](https://cdn.numerade.com/previews/b0a91243-1218-48d3-b16c-6ac90d89a6d6_large.jpg)
SOLVED: a) Suppose a random variable X has the moment generating function MX(t) := E[e tX]. Let g(t) := log MX(t), then prove that g 00(0) = Var[X]. (b) Suppose a random
![SOLVED: Proof: We prove this theorem by first computing the moment generating function and finding out the mean and variance of X from it M(t) = E(etX) = etr f(r) dr 1 =/ SOLVED: Proof: We prove this theorem by first computing the moment generating function and finding out the mean and variance of X from it M(t) = E(etX) = etr f(r) dr 1 =/](https://cdn.numerade.com/ask_images/0cd621250453447aaf92bc2d0041c5b0.jpg)