Let y follow a normal distribution with unknown mean 0 and known standard deviation (i.e. y ~ N(0,)) and place a N(, ) prior on 0. Confirm that the posterior distribution for 0 is: ely ~ N (+y +2 0+12 and show that the posterior precision is the sum of the precisions in the likelihood and the prior, where the precision is defined as the reciprocal of the variance. Hint: you will need to 'complete the square' to find the final form of the posterior mean and variance for 0.