If X|0 ~ Bin(n, 0) and 0 Beta(a, B), show that the posterior distribution of 0 given X is a beta distribution with parameters x + a and n-x+B. Note: r(a + B) f(x|0) = ) 0*(1– 0)"-x -ga-1(1– 0)B-1 аnd h(8) %3D r(a)r(B)

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If X|0 ~ Bin(n, 8) and 0 - Beta(a, B), show that the posterior distribution of 0 given
X is a beta distribution with parameters x + a and n-x +B.
Note:
f(x\0) = () 0*(1– 0)"-*
Г(а + В)
h(0)
Г(а)Г()
ea-1(1 – 0)B-1
and
Transcribed Image Text:If X|0 ~ Bin(n, 8) and 0 - Beta(a, B), show that the posterior distribution of 0 given X is a beta distribution with parameters x + a and n-x +B. Note: f(x\0) = () 0*(1– 0)"-* Г(а + В) h(0) Г(а)Г() ea-1(1 – 0)B-1 and
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