Normal Distribution Mean and Variance Proof
In this video we derive the Mean and Variance of the Normal Distribution from its Moment Generating Function (MGF).
We start off with reminding ourselves of the MGF of the Normal Distribution and then proceed to derive the first moment E[X]. After we have done this we proceed to derive the second moment E[X^2], and then lastly we derive the Variance of the Normal Distribution using these two results.
#Normal
#Mean
#Variance
0:00 Introduction
0:59 Deriving the Mean
2:45 First Moment Derived
2:52 Deriving the Variance
8:11 Second Moment Derived
8:47 Variance Derived