If Z1, Z2 and Z3 are 3 independent standard normal variates, then what

1.	If Z1, Z2 and Z3 are 3 independent standard normal variates, then what is the distribution of Z12 + Z22 + Z32?
Answer» Here Z₁² + Z₂²+ Z₃² is a chi-square distribution with 3 degrees of freedom, i.e., χ(3)² Variance = 2n = 2.3 = 6.

If Z1, Z2 and Z3 are 3 independent standard normal variates, then what is the distribution of Z12 + Z22 + Z32?

Answer»

Here Z₁² + Z₂²+ Z₃² is a chi-square distribution with 3 degrees of freedom,

i.e., χ(3)² Variance = 2n = 2.3 = 6.