Jul 22, 2024 · Let $X \sim \ContinuousUniform a b$ for some $a, b \in \R$ denote the continuous uniform distribution on the interval $\closedint a b$. Then the moment generating function of …

Attempting to calculate the moment generating function for the uniform distrobution I run into ah non-convergent integral. Building of the definition of the Moment Generating Function $ M (t) = …

Sep 25, 2019 · Definition 6.1.1. The moment-generating function (mgf) of the (dis-tribution of the) random variable Y is the function mY of a real param-eter t defined by mY(t) = E[etY],

Jul 26, 2025 · Moment Generating Function (MGF): It is used to calculate the moments of a distribution, which are useful in understanding the central tendency (mean), spread (variance), …

If the moment-generating function () exists for in an open interval containing 0, like (− 0, 0), for some 0 > 0, then it uniquely determines the probability distribution.

Moment-generating function In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.

The uniform distribution explained, with examples, solved exercises and detailed proofs of important results

Sep 2, 2025 · Uniform Distribution: Moment Generating Function by Anthony Morciglio Last updated 2 months ago Comments (–) Share Hide Toolbars

Not only can a moment-generating function be used to find moments of a random variable, it can also be used to identify which probability mass function a random variable follows.

When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of how sensitive the tests are to heavy-tail departures …