Probability - Getting joint distribution?

  • Thread starter Kuma
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  • #1
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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
 

Answers and Replies

  • #2
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 ?
 
  • #3
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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!
 
  • #4
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).
 
  • #5
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yes thats what i meant, normal with mean 0 with variance 1.
 
  • #6
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 ]
 
  • #7
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Thanks for your help, but its not actually what my question is looking for. This is the question.

Untitled.png


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, im not sure if im doing it right. The change of Variable for my Y is quite large.
 

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