# Math Help - Moment Generating Function

1. ## 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).

2. 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.

3. 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.

4. 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

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

I've been taught everything in that wikipedia page except the covariance.

6. Originally Posted by Hitman6267
It's $P(1 \leq X \leq 2)$

I've been taught everything in that wikipedia page except the covariance.
Then you have to calculate Pr(X = 1) + Pr(X = 2). And you do that using the pmf for a binomial variate with parameters n = 5 and p = 0.7.