Suppose that data x Rd, y = {0,1} is generated according to the following process: first, y is sampled from a Bernoulli distribution with parameter q = (0, 1) (that is, y is 1 with probability q and 0 with probability 1 q). Then, each feature x, is sampled independently from a Gaussian distribution with mean o if y=0, or with mean 1 if y = 1, and variance ; (the variance is the same no matter the value of y). Prove that p(y = 1|2) is a logistic function, i.e. 1 P(y = 1x)= == 1+ eT+Bo Derive expressions the the intercept Bo and the weights in terms of the feature means jo, j1, variances , and Bernoulli parameter q.