- #1
SithV
- 5
- 0
Hi people!
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 here's 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!=(
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 here's 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!=(