# Math Help - Moments

1. ## Moments

The random variable X has an exponential distribution with parameter b. It is found that Mx(-b^2) = 0.2
Find b
****************
No idea really...

Given: Mx(-b^2) = Ex(e^(-tb^2)) = 0.2

General exponential mgf: Mx(t) = b/(b-t)

Thanks !

2. ## Re: Moments

The random variable X has an exponential distribution with parameter b. It is found that Mx(-b^2) = 0.2
Find b
****************
No idea really...

Given: Mx(-b^2) = Ex(e^(-tb^2)) = 0.2

General exponential mgf: Mx(t) = b/(b-t)

Thanks !
$M_X(t)=\dfrac{b}{b-t}\implies M_X(-b^2)=\dfrac{b}{b-(-b^2)}=\dfrac{1}{1+b}$ and you can use the given condition to find b.

If you still have trouble, try using the defintion of mgf

$M_X(-b^2)=\int_0^{\infty}\exp(-b^2x)\times b \times \exp(-bx)\;dx$

and integrate

3. ## Re: Moments

Thank you ! I should have known that