4. [20 marks] Let D = {apple, orange, pear} and ? be the set of all functions from D to {1, 2,3}. Define a probability P on ? by P({f)) = maxIED f(@) 72 , for every f : D - {1, 2, 3}. The numerator here is the maximum among f(apple), f(orange) and f(pear). Define a random variable X on ? by X(f) = f(apple) + f(orange). Compute the expectation of X