elmarsur said:Thank you very much, LC!
I imagine that there isn't any significant difference between MGF and PGF (probability), the latter being a special application of the first?!
If so, I still have a couple of questions:
1) Do the formulae apply to all sorts of probability distributions/densities?
2) How do I calculate the variance (formula-wise) for these generating functions (which I understand are not really functions but series of terms)?
Thank you very much in advance.
A probability generating function is a mathematical tool used to describe the probability distribution of a discrete random variable. It is a power series that represents the probabilities of all possible outcomes of the random variable.
A probability generating function is specific to discrete random variables, while a moment generating function can be used for both discrete and continuous random variables. Additionally, the coefficients in a probability generating function represent probabilities, while the coefficients in a moment generating function represent moments of the random variable.
A probability generating function allows us to easily calculate various properties of a discrete random variable, such as its expected value and variance. It also allows us to determine the probability of specific outcomes or events occurring.
The probability generating function is calculated by taking the sum of pixi for all possible values of the random variable, where pi is the probability of the random variable taking on the value i. This can also be expressed as the expected value of xs, where s is a variable.
No, a probability generating function can only be used for discrete random variables. For continuous random variables, we use a moment generating function or a probability density function to describe the probability distribution.