Probability - Getting joint distribution?

[Kuma]

Homework Statement

I have 2 variables that are both i.i.d. X1 and X2.
i.i.d means they both have the same distribution and are independent of each other.

My question is, how do i get the joint distribution:
Fx1,x2(x1,x2) of these variables??

Homework Equations

The Attempt at a Solution

no idea where to start

 

[╔(σ_σ)╝]

What other information do you have.

Indepence tells you that

Fx1,x2(x1,x2) = Fx1(x1) * Fx2(x2)

So the joint CDF is the product of the marginal CDF's.Do you have the joint PMF or PDF ?

 

[Kuma]

Actually I was just generalizing an assignment question, i needed this to start the question entirely. x1,x2 are both N~(0,1).

Thanks for your answer!

 

[╔(σ_σ)╝]

I am not familiar with the notation N~(0,1).

I assume you mean normal distributions with mean of 0 and variance of 1.

You can find the formula for the joint PDF and then find the marginal PDF for x1 and then differentiate to get Fx1(x1).

 

[Kuma]

yes that's what i meant, normal with mean 0 with variance 1.

 

[╔(σ_σ)╝]

Well get your joint pdf and then differentiate it to get the CDF Fx1,x2(x1,x3)

Look for the formula for a bivariate Gaussian random variable.

p =0 [ since we have independence ]

 

[Kuma]

Thanks for your help, but its not actually what my question is looking for. This is the question.

Now i need to get Fz1,z2(z1, z2) so i could do a change of variable and use that formula with the jacobian to get the bivariate normal.
Kinda got stuck in some of the calculations though, I am not sure if I am doing it right. The change of Variable for my Y is quite large.