Question

Let Θ be a continuous random variable that represents the unknown bias (i.e., the probability of Heads) of a coin.

a) The prior PDF fΘ for the bias of a coin is of the form

fΘ(θ)=aθ9(1−θ),   for θ∈[0,1],

where a is a normalizing constant. This indicates a prior belief that the bias Θ of the coin is

b) We flip the coin 10 times independently and observe 1 Heads and 9 Tails. The posterior PDF of Θ will be of the form cθm(1−θ)n, where c is a normalizing constant and where

m=

n=

Answer 1