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(b) Consider a regression problem in which we aim to predict a single dependent variable t from a single independent variable x. It is known that the true data generating function is t = h(x) + c. where h(x) = c. a constant, and e is normally distributed with mean 0 and variance o? = 1/2. We would like to estimate the value of c by fitting a model f(x, w) = w using Bayesian regression. Our estimate for w provides an estimate for c. The prior distribution of w is assumed to be p(w) ox exp(-w?). A single data point X = (x. t) = (3, 10) is known. (i) In the absence of data, what is E[w] (the expected value of w)? (ii) Write down the likelihood of the data point X. (iii) Write down the posterior distribution of w given data point X