Question

Let X U(0,theta). Find the moment generating function of X and show how to use it to find the mean and variance of X.

I think this follows the uniform distribution so..

mean = (theta1 + theta2)/2

variance = [(theta2- theta1)^2]/ 12

moment generating function = [e^(t*theta2) - e^(t*theta1)]/(t * (theta2-theta1))

I think the beginnning of the problem means that theta1 is 0? I'm not sure how to show the moment generating function.

Answer 1

Kristi u r correct theta1 is 0

∴ MGF = (e^(t*theta) - 1 )/(t*theta)

let theta =θ

mean = firat derivative of MGF at t=0

Variance = (second derivative of MGF at t=0) - (mean^2)