2. Assume that an airplane engine will fail in flight with probability 1 - p independently of the plane's other engines. (An engine functions normally with probability p.) Also assume that a plane can successfully complete its flight if at least half of the engines are functional. Let X denote the number of engines that do not fail. (a) Consider a 2- engine plane. What type of random variable is X? Indicate both the type and the appropriate parameters using the "" notation. Write down the pdf of X, and do not forget to indicate the range of values that X can take on. Your answer will involve the parameter p. (b) What is the probability that a 2- engine plane will complete its flight? (c) Now consider a 4- engine plane. Write down the pdf of X, and do not forget to indicate the range of values that X can take on. (d) What is the probability that a 4- engine plane will complete its flight? (e) Under what simple condition on p is a 4- engine plane preferable to a 2- engine plane? You might use WolframAlpha to solve the inequality