distribution with changed parameters

Question 3
a)
( | )( | ) ∏ ( | )( | ) ( )
∏ ( | )( | ) ∏( ) ∑ ( ) ∑
∏( )
So, the multiplication can be shown as

( | )( | ) ∑ ( ) ( ) ( )

( ) ∑ ( )
Where it simplifies as
( | )( | )
( )
( ) ( )
∑ ( ) ∑
It can be seen that posterior distribution looks like a beta distribution with changed parameters
As
(∑ ∑ )
So it can be said that since the posterior and prior are from the same family of distributions the prior
is infact a conjugate prior
b)

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