# Questions tagged [moment-generating-function]

A description of a probability distribution which is related to the Laplace transform. Use also for its logarithm, the cumulant generating function.

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### what is the formula for calculation of fourth raw moment (or central moment) from variance and 3rd central moment (or raw moment)?

Basically the title. I can't seem to find any solution for this. I have the mean, variance or the second central moment and third central moment and third raw moment. I need to find the fourth raw ...
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### How to find probability from $E[X^n]$?

It is given that $E[X^n] = \frac{2}{5}(-1)^n + \frac{2^{n+1}}{5}+\frac{1}{5}$, where $n=1,2,3,\ldots.$ I need to find $P(|X-\frac{1}{2}| > 1)$. What my approach is : I have opened the modulus ...
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### The distribution function of the min of two random variables which are dependent via a common term

Consider the following two random variables: $$Z_1=U_1-X_1$$ and $$Z_2=U_2-X_1,$$ where $U_1$ and $U_2$ are two i.i.d random variables following a general distribution, and $X_1$ is an exponential ...
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### Confirmation of MGF of Shifted Exponential Distribution

Consider the probability distribution $D \sim X - a$ where $X \sim \text{Exp}(\lambda)$. My task is to find the MGF of probability distribution $D$. I think I have a solution but it contradicts what I ...
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