1. ## MGF

For the random variable:
P(Y=0)= 1/8, P(Y=1)=1/2, P(Y=3)=3/8
Find the MGF of Y, and E[Y] and Var(Y).

Helpppp, I reallly don't have a clue how to do this!

2. Originally Posted by georgiahelo
For the random variable:
P(Y=0)= 1/8, P(Y=1)=1/2, P(Y=3)=3/8
Find the MGF of Y, and E[Y] and Var(Y).

Helpppp, I reallly don't have a clue how to do this!
If X is a finite random variable taking on values x1, x2, . . ., xn, the mean or expected value of X, written μ, or E(X), is
μ = E(X) = x1.P(X = x1) + x2.P(X = x2) + . . . + xn.P(X = xn) = ∑ (xi.P(X = xi))If X is a random variable, its variance is defined to be
σ2 = E( [X - μ]2 ). Its standard deviation is defined to be the square root σ of the variance.

replace X by Y ...

3. Originally Posted by georgiahelo
For the random variable:
P(Y=0)= 1/8, P(Y=1)=1/2, P(Y=3)=3/8
Find the MGF of Y, and E[Y] and Var(Y).

Helpppp, I reallly don't have a clue how to do this!
Start by applying the defintions!

By definition of MGF: $m(t) = E(e^{tY}) = \frac{1}{8} + \frac{1}{2} e^t + \frac{3}{8} e^{3t}$.

By definition: $E(Y) = \left. \frac{dm}{dt}\right|_{t = 0} = ....$

By definition: $Var(Y) = E(Y^2) - [E(Y)]^2$. And by definition $E(Y^2) = \left.\frac{d^2m}{dt^2}\right|_{t = 0} = ....$

4. ## MGF's

Thankyou, I think I've done it now!
I have another question!
If Y1 and Y2 are independent random variables with the same PMF as the original posted question, how do I find the MGF of W=Y1+Y2?

5. Originally Posted by georgiahelo
Thankyou, I think I've done it now!
I have another question!
If Y1 and Y2 are independent random variables with the same PMF as the original posted question, how do I find the MGF of W=Y1+Y2?
You're expected to know the theorem given here regarding the moment generating function of a sum of independent random variables: Moment-generating function - Wikipedia, the free encyclopedia