The density function of Students distribution on degrees of freedom is (1+t 2/) (+1)/2 1/2B(

The density function of Student’s distribution on ѵ degrees of freedom is

(1+t 2/ν)

−(ν+1)/2

ν

1/2B(

1 2

,ν/2) − ∞ < t < ∞, r − 1 j − 1 r − 1 j − 1 r − 1 j − 1

μ

′

r =

r ∑

j=0

( )μr−j(μ

′

1)

j

μr =

r ∑

j=0

( )μ

′

r−j(−μ

′

1)

j

.

r j

r j

where B(.,.) is the beta function. Show that the odd moments that exist are zero and that the even moments are

.

Hence show that