Suppose that you purchased a smartphone some time in the past. you are told that the number of years from when it was purchased till when it fails is a random variable with distribution exp(1/4) (regardless of when it was purchased). now, suppose that the smartphone happens to fail today. we wish to estimate how long ago it was purchased. let x represent the number of years ago it was purchased (so x > 0 a. let y represent the observation of when it failed, relative to today, so the given observation is y = 0; if the failure were to have taken place 1 year ago, we would have y = -1. assume that the a priori distribution of x is uniform on [3,6]. a. find fy|x (y|x) for x > =0. b. find the maximum-likelihood estimate of x given y = 0. c. find the minimum mean-squared-error estimate of x given y = 0. d. find the maximum a posteriori probability estimate of x given y = 0. e. find the linear minimum mean-squared-error estimate of x given y = 0.