Let X have density fX (x) 1 2r /2 r 2 xr /21 exp x 2 for x

Let X have density fX (x) Æ

1 2r /2¡

¡ r 2

¢ xr /2¡1 exp

³

¡

x 2

´

for x ¸ 0. This is known as the chi-square distribution. Let Y Æ 1/X. Show that the density of Y is fY (y) Æ

1 2r /2¡

¡ r 2

¢ y¡r /2¡1 exp

µ

¡

1 2y

¶

for y ¸ 0. This is known as the inverse chi-square distribution.