Hi people!(adsbygoogle = window.adsbygoogle || []).push({});

Im having problems with my Prob.Theor. assignment=(

I was hoping that u might be able to help me...

I have 2 problems that i ve no idea how to solve!Oo

Heres 1st one

We re given rand. var. X, its mean value U, the stand deviation S (sigma).

We need to show that E(z)=0 and var(z)=1

if the relation between X and Z is this eq. Z=X-U/S

2nd

Show if a rand. var. has the prob. density

f(x)=1/2*Exp[-lxl] -inf<X<inf

lxl-abs value

then its moment gen func. is

Mx(t)=1/1-t^2

im not sure about this one bu heres what i got

we re using the formula from the definition

and gettin this

1/2(Int[Exp[tx]*Exp[-lxl]) -inf<X<inf

but lxl=+-x

then we get 2 integrals

1/2(Int[Exp[tx]*Exp[-x])

and

1/2(Int[Exp[tx]*Exp[x])

both in -inf<X<inf

now if we integrate it we get

1/2Exp[x(t-1)]/t-1

and

1/2Exp[x(t+1)]/t+1

both in -inf<X<inf

whats next?=(

Would appreciate any help!=(

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Moments and Moment-gen. function.

**Physics Forums | Science Articles, Homework Help, Discussion**