Thread: Derive the moment-generating function of Y bar

Suppose that Y1, Y2, …, Yn are independent, normally distributed random variables with mean u and
variance . Define



Derive the moment-generating function of Y bar

Originally Posted by wopashui

Suppose that Y1, Y2, …, Yn are independent, normally distributed random variables with mean u and
variance . Define



Derive the moment-generating function of Y bar

What have you tried? Where are you stuck?

Originally Posted by mr fantastic

What have you tried? Where are you stuck?

srooy, i don't know how to start the question, do i start by definition m(t)= E(e^tybar)= integral e^tybar times f(y) then sub in the summation into the integral, but what is f(y)here, do we use the normal density function?

Originally Posted by wopashui

srooy, i don't know how to start the question, do i start by definition m(t)= E(e^tybar)= integral e^tybar times f(y) then sub in the summation into the integral, but what is f(y)here, do we use the normal density function?

Given!!:

Yn are independent, normally distributed random variables with mean u and
variance img.top {vertical-align:15%;} .

well linear combo's of normals is a normal, hence just compute moo and sigma squared of y bar.

Originally Posted by matheagle

well linear combo's of normals is a normal, hence just compute moo and sigma squared of y bar.

then how do you find the mgf with moo and the variance, we know that m'(0)=moo, and m''(0)-[m'(0)]^2= variance