Moment Generating Function

• Jul 10th 2010, 10:13 AM
Hitman6267
Moment Generating Function
I have a problem that gives me a M.G.F and asks for P(1< or = X < or = 2)

For example M(t)= $(0.3 + 0.7 e^t)^5$

P(1< or = X < or = 2) = 0.1607

How is that done? I can't find the principle in my text.
I know that P(2) is equal to M(2) but how about the above example ?

Edit: If possible please post a link to a a page that explain how to use M.G.F , I'm having problems with various applications. Like how to get the M.G.F from E(X).
• Jul 10th 2010, 04:08 PM
mr fantastic
Quote:

Originally Posted by Hitman6267
I have a problem that gives me a M.G.F and asks for P(1< or = X < or = 2)

For example M(t)= $(0.3 + 0.7 e^t)^5$

P(1< or = X < or = 2) = 0.1607

How is that done? I can't find the principle in my text.
I know that P(2) is equal to M(2) but how about the above example ?

Edit: If possible please post a link to a a page that explain how to use M.G.F , I'm having problems with various applications. Like how to get the M.G.F from E(X).

You're meant to recognise this as the mgf of a random variable that follows a binomial distribution. Your job is to get from it the values of n and p, and then to use the now known mass density function to calculate the required probability.
• Jul 11th 2010, 01:25 AM
Hitman6267
Quote:

Originally Posted by mr fantastic
You're meant to recognise this as the mgf of a random variable that follows a binomial distribution. Your job is to get from it the values of n and p

I was able to do that.
n=5
p=0.7

But what does P(1< or = X < or = 2) mean ? The probability of what ?
Also unless I'm mistaken we haven't learned the mass density function.
• Jul 11th 2010, 03:35 AM
mr fantastic
Quote:

Originally Posted by Hitman6267
I was able to do that.
n=5
p=0.7

But what does P(1< or = X < or = 2) mean ? The probability of what ?
Also unless I'm mistaken we haven't learned the mass density function.

Well, I have no idea what P(1< or = X < or = 2) means. It would help if you typeset your equation properly using latex. From what I can understand, P(1< or = X < or = 2) might mean $\Pr(1 \leq X = 2)$, which would give an answer of zero because you cannot be equal to 2 and less than or equal to 1. But I doubt that's what the original question intends.

By the way, are you saying that you know nothing given here: Binomial distribution - Wikipedia, the free encyclopedia
• Jul 11th 2010, 03:42 AM
Hitman6267
It's $P(1 \leq X \leq 2)$

It's $P(1 \leq X \leq 2)$