The probability density function of the normal distribution is given by 1 f(x; , o) (x-)2 == exp 22 202 where is the mean and o is the variance of the distribution. (a) [20 marks] Assuming that = 0, derive the maximum likelihood estimate of o given the sample of i.i.d data (x1, x2,...,xT).|. (b) [20 marks] Now assume that x is conditionally normally distributed as N(0,0%), where = =w+ Bo 1 + x-1 Write down the likelihood function for this model given a sample of data (x1, x2, ..., TT).