(Sonar) A scientist is trying to determine the depth of the sea at a certain location. She knows that it must be deeper than 5 km but that is all she knows. To capture this uncertainty she models the depth as uniformly distributed between 5 and 10 km. In order to measure the depth she uses sonar, taking 2 measurements, which we model as two random variables 1 and 32. If the depth is equal to :c then each sonar measurement is uniformly distributed between cc 0.25 and :1: + 0.25. The two measurements are conditionally independent given the depth. (a) Compute and sketch the pdf of the rst sonar measurement E1. 2 b) Compute the conditional pdf of the depth conditioned on the measurements being equal to 7 km and 7.1 km. c) Compute the joint pdf of the two sonar measurements 1 and E2. Are the two measurements independent? Justify your answer mathematically and explain it in tuitively