The RVs X and Y are independent with Rayleigh densities: Find the densities of the following...

Question

Question

The RVs X and Y are independent with Rayleigh densities: Find the densities of the following RVs. (b) W2

Answer 1

Answer #1

a)

here σ = 1

X^2 follow chi-squared distribution with parameter degree of freedom 2

similarly Y^2 follow chi-squared distribution with parameter degree of freedom 2

Z = X^2 + Y^2 follow chi-square with degree of freedom = 2 +2 = 4

b)

W is ratio of two chi-square distribution with same degree of freedom

hence

W follow F-distribution with df1 = 2 , df2 = 2

Answer 2

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