- #1
sneaky666
- 66
- 0
Homework Statement
Let Y=x+4. Compute rY(t) in terms of rX
Homework Equations
The Attempt at a Solution
is the answer just
r 3X+4 (t)
?
A probability generating function is a mathematical tool used in probability theory to model the probability distribution of a discrete random variable. It is a power series that generates the probabilities of all possible outcomes of a 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, a probability generating function only generates the probabilities of outcomes, while a moment generating function generates the moments of a distribution.
The main purpose of using a probability generating function is to simplify calculations and make it easier to analyze the behavior of a random variable. It allows for the calculation of probabilities without having to use complex formulas or tables.
The probability generating function is related to the moments of a distribution through its derivatives. Specifically, the k-th derivative of the probability generating function evaluated at 1 gives the k-th moment of the distribution.
No, a probability generating function is only defined for discrete random variables. For continuous random variables, a moment generating function or a characteristic function is typically used instead.