3. (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 E1 and g. If the depth is equal to :1: then each sonar measurement is uniformly distributed between a: 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 1. 2 (b) Compute the conditional pdf of the depth conditioned on the measurements being equal to 7 km and 7.1 km. (0) Compute the joint pdf of the two sonar measurements 3'1 and 2. Are the two measurements independent? Justify your answer mathematicay and explain it in- tuitively