Let X and Y be independent random variables distributed respectively as chi^(2)(m) and chi^(2)(n). Find the density of Z=X/(X+Y).

Koronicaqn

Koronicaqn

Answered question

2022-09-11

Let X and Y be independent random variables distributed respectively as χ 2 ( m ) and χ 2 ( n ). Find the density of Z = X/(X + Y).

Answer & Explanation

Kathleen Mack

Kathleen Mack

Beginner2022-09-12Added 9 answers

We are given that X χ 2 ( m ) Г ( m 2 , 1 2 )
Y χ 2 ( n ) Г ( n 2 , 1 2 )
where the last equalities in each row are definitions of chi-squared distribution.
X X + Y B e t a ( m 2 , n 2 )
Result:
X X + Y B e t a ( m 2 , n 2 )

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