In addition to responding to the questions on this assignment, please tell us approximately how much time you spent on each question. Thanks! Question 1. Bayes's Rule is often used in "Bayesian updating", since it is used to take a prior probability distribution and update it on the basis of observed evidence to produce a posterior distribution. Before, after, hence updating; get it? This notion of "Bayesian updating" is particularly useful when applied iteratively. Consider a scenario where we have a prior distribution P(H) over hypotheses, and then we observe evidence E1 and use Bayes's Rule to update our distribution to P(HE1)=P(E1)P(E1H)P(H) The distribution P(HE1) can now be viewed as a new, more informed prior. Therefore if we see a new piece of evidence E2, we can use Bayes's Rule again to derive a new posterior. Since P(HE1) is the prior now, the result will take the form P(HE1,E2)=YXP(HE1) Derive the simplest possible form of the full expression, i.e. fill in X and Y, assuming that E1 and E2 are independent. Please show your work. (Note that if you don't make that assumption, you won't get the right answer. Also recall that "independent" and "conditionally independent given some variable" are two different things..) Please don't forget to tell us approximately how much time you spent on this