Help with this easy exercise

[EcoEco]

Hello,

I need help with the following exercise. I don´t know how to solve it. Thanks a lot.

X=0.7Z
Y=1.7 + 0.4Z
μz=9 σz=3

E[(x-μx)·(y-μy)] ?

 

[obh]

E (aX+b) =aE(X)

 

[EcoEco]

Sorry but I already cant answer the problem

I have some thoughts:

E(x-μx)=E(x)-E(μx)=4-4=0
E(x)=E(0.7z)=0.7E(z)=0.7·8=5,6
E(μx)=μx=E(x)=E(0.7z)=0.7E(z)=0.7·8=5.6

I think this reasoning is incorrect

 

[obh]

You need to set Z into X and Y,
Also use the following formula: σ^2=e(x^2)-(e(x))^2

 

[Dason]

E (aX+b) =aE(X)

That's missing something

 

[obh]

That's missing something

Typo I'm sure I wrote : E (aX+b) =aE(X)+b

 

[obh]

Hi Eco , as you state it is really easy ... did you manage?
You just need to keep the full equation, set z into X and Y, and do basic algebra, then use the 2 formulas E(aX+b) and E(x^2).
{Z instead of X in your case}

You can't separate the equation (like you separated E(x-μx) ) as there is a multiplication of random variables

 

[EcoEco]

Ok, now I can do it, thanks

 

[obh]

Great, let me know what you got