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Suppose Y = X^2 + Z^2,where X , Z are both normally distributed, but they are...

Suppose Y = X^2 + Z^2,where X , Z are both normally distributed, but they are not independent. What is the distribution of Y?

Exponential Distribution
Normal distribution
Chi Square distribution
None of the other answers
math   Statistics-And-Probability   
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Answer #1

If standard normal variates are independent and their sum of squares leads to chi square distribution

But here X and Z are both normally distributed where they are not independent.

Y = X^2 + Z^2

Distribution of Y is Normal distribution.

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