Howtosignalprocessing
- What do you mean by moment generating function of a random variable?
- What is the difference between moment generating function and characteristic function?
- What is the meaning of moment generating function?
- Why are moment generating functions important?
What do you mean by moment generating function of a random variable?
The moment generating function (MGF) of a random variable X is a function MX(s) defined as MX(s)=E[esX]. We say that MGF of X exists, if there exists a positive constant a such that MX(s) is finite for all s∈[−a,a].
What is the difference between moment generating function and characteristic function?
A characteristic function is almost the same as a moment generating function (MGF), and in fact, they use the same symbol φ — which can be confusing. Furthermore, the difference is that the “t” in the MGF definition E(etx) is replaced by “it”.
What is the meaning of moment generating function?
The moment-generating function is the expectation of a function of the random variable, it can be written as: For a discrete probability mass function, For a continuous probability density function, In the general case: , using the Riemann–Stieltjes integral, and where is the cumulative distribution function.
Why are moment generating functions important?
Helps in determining Probability distribution uniquely:
Using MGF, we can uniquely determine a probability distribution. If two random variables have the same expression of MGF, then they must have the same probability distribution.
