Math Problem Statement
Suppose Y is a random variable with cumulant generating function (cgf)
K Y ( t )
e t − 1.
What is the distribution of Y ?
N(0,1)
exponential (1)
Poisson(1)
U(0,1)
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability Theory
Cumulant Generating Function
Poisson Distribution
Formulas
K_Y(t) = e^t − 1
K_Y(t) for Poisson(λ) = λ(e^t − 1)
Theorems
Poisson Distribution CGF Theorem
Suitable Grade Level
Undergraduate Probability and Statistics
Related Recommendation
Exponential Random Variable and Poisson Distribution: Calculating P(Y=1) and Expected Value
Moment Generating Functions for Normal and Poisson Distributions
Moment Generating Function for a Geometric Random Variable with PMF
Probability Distribution Function of Y = X1 + X2 | Poisson Distribution
Deriving the Moment-Generating Function for a Binomial Distribution