Let X have density fX (x) 1 2r /2 r 2 xr /21 exp
Question:
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.
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