## How do you find the factorial moment generating function?

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The factorial moments can be computed from the derivatives of the probability generating function. The factorial moments, in turn, determine the ordinary moments about 0 (sometimes referred to as raw moments ). Suppose that the radius of convergence . Then P ( k ) ( 1 ) = E [ N ( k ) ] for k ∈ N .

## What is joint moment generating function?

Similarly to the univariate case, a joint mgf uniquely determines the joint distribution of its associated random vector, and it can be used to derive the cross-moments of the distribution by partial differentiation.

**How do you find the joint MGF?**

Definition: MGF of (X,Y) Let X and Y be two RVs with joint pdf f(x,y) then the MGF of X & Y: Theorem: The MGF of a pair of independent RVs is the product of the MGF of the corresponding marginal distributions. That is, mXY(t1,t2) = mX(t1) mY(t2).

### What is E and VAR?

The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.

### What is factorial moments in statistics?

In probability theory, the factorial moment is a mathematical quantity defined as the expectation or average of the falling factorial of a random variable.

**How do you find Ex and Ey?**

To obtain E(XY), in each cell of the joint probability distribution table, we multiply each joint probability by its corresponding X and Y values: E(XY) = x1y1p(x1,y1) + x1y2p(x1,y2) + x2y1p(x2,y1) + x2y2p(x2,y2).

## Can factorial be distributed?

A factorial distribution happens when a set of variables are independent events. In other words, the variables don’t interact at all; Given two events x and y, the probability of x doesn’t change when you factor in y.