5 Probability (a) A probability density function is dened by f(:r) = {Cem ifs: > 0, 0 otherwise. (i) (1 point) Find the value of C that makes f (x) a valid probability density function. (ii) (1 point) Compute the expected value of m, i.e., E(:r). (b) (2 points) Three locks are randomly matched with three corresponding keys. What is the probability that at least one lock is matched with the right key? (c) Bayes Rule (2 points) There is a 10% chance that a thunderstorm is approaching at any given moment. You own a dog that has a 75% chance of barking when a thunderstorm is approaching and only a 25% chance of barking when there is no thunderstorm approaching. If your dog is currently barking, how likely is it that a thunderstorm is approaching