Thread: [SOLVED] Moment Generating Function

Consider a discrete random variable X with the probability mass function as:
x 2 4 6 8 10 16
P(x) 0.1 0.2 0.35 0.2 0.1 0.05


Find the moment generating function of X.


Do I set it up as this?
0.1e^2t + 0.2e^4t + 0.35e^6t + 0.2e^8t + 0.1e^10t + 0.05e^16t
If so, what do I do from there? I feel like I'm on the total wrong track here.

Originally Posted by ban26ana

Consider a discrete random variable X with the probability mass function as:
x 2 4 6 8 10 16
P(x) 0.1 0.2 0.35 0.2 0.1 0.05


Find the moment generating function of X.


Do I set it up as this?
0.1e^2t + 0.2e^4t + 0.35e^6t + 0.2e^8t + 0.1e^10t + 0.05e^16t
If so, what do I do from there? I feel like I'm on the total wrong track here.

Yes. Your answer is correct.

You could simplify by taking out a common factor of but I don't see why you'd bother.

So that's the final answer? For the rest of the problems, I got t<-ln(?), where the ? was a number like 0.1. Is my final answer for this the long equation that I typed? I just confused myself.

Originally Posted by ban26ana

So that's the final answer? For the rest of the problems, I got t<-ln(?), where the ? was a number like 0.1. Is my final answer for this the long equation that I typed? I just confused myself.

I said your answer was correct, didn't I? As for the rest of the problems, I can't comment on what I can't see.

Originally Posted by mr fantastic

I said your answer was correct, didn't I? As for the rest of the problems, I can't comment on what I can't see.

Thanks. I guess it just didn't look right to me. But then, if I knew what I was doing, I wouldn't be on here asking questions.