Moment : core role in describing distributions.
1. make a moment generating function --- Mx(t)
2. differentiate it 'r'th time ---M'r(t)
3. t=0 --- M'r(0) = E(X^r)
Moment Generating Function (MGF) :function that generates 'Moments'
<Moment generating function of Bernoulli distribution >
<Moment generating function of Binomial distribution>
<Moment generating function of Exponential distribution >
<Moment generating function of Standard Normal distribution>
<Moment generating function of Geometric distribution >
<Moment generating function of Poisson distribution>
<Moment generating function of Gamma distribution>
<Moment generating function of Chi-squared distribution >
<Moment generating function of Uniform distribution >
<Moment generating function of Beta distribution >
Properties of Moment Generating Function (MGF)
'Uniqueness' means ' If X and Y has same moment generating function, X and Y have same distribution'
Joint Moment Generating Function
Joint Moment Generating Function <Independent>
You can easily find Joint moment generating function of X and Y with multiplying moment generating function of X with Y when they are independent.
Joint Moment Generating Function <dependent>
