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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!=(

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# Moments and Moment-gen. function.

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