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

a) The prior PDFf

for the bias of a coin is of the form

f()=a9(1),for[0,1],

wherea is a normalizing constant. This indicates a prior belief that the bias of the coin is : select :high??? Low???

b) We flip the coin 10 times independently and observe 1 Heads and 9 Tails. The posterior PDF of

will be of the formc^m(1)ⁿ, wherec is a normalizing constant and where

M= ????

N= ????