Thread: Moment generation function

Hi,

I was given a moment generating function M(t) = (1-t)^-3

However, I'm told to compute P (-5 < X < 4) if I can (or explain if I can't compute).

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If I'm not wrong the random variable (X) is gamma with parameters (2,1).

But X must be at least 0. So does do I compute P (-5 < X < 4) = P (0 < X < 4) ? Or is it un-computable? If so, how do I explain?

Can anyone help? Thanks.

Hello,

Originally Posted by knighty

Hi,

I was given a moment generating function M(t) = (1-t)^-3

However, I'm told to compute P (-5 < X < 4) if I can (or explain if I can't compute).

---

If I'm not wrong the random variable (X) is gamma with parameters (2,1).

But X must be at least 0. So does do I compute P (-5 < X < 4) = P (0 < X < 4) ? Or is it un-computable? If so, how do I explain?

Can anyone help? Thanks.

It's a Gamma, but I think it's rather (3,1) than (2,1) (I checked it in wikipedia )

You're correct to say that P(-5<X<4)=P(0<X<4)
You can even say that it's P(X<4), where X follows $\displaystyle \Gamma(3,1)$

So you're looking for the value of the cumulative density function of Gamma(3,1) : $\displaystyle F(4;3;1)=1-\sum_{i=0}^2 \frac{4^i}{i!} e^{-4}$
Look here : Gamma distribution - Wikipedia, the free encyclopedia