below is the question

(Expectations) Select five random numbers X1, X2, X3, X4, X5 independently according to a continuous distribution f over R. Note that since f is continuous, all points will be different. The ith point is a local maximum if it is larger than its immediate neighbors. For example, if the five points are 1.3, 2.3, 1.7, 3.5, 4.2, then there are two local maxima: the second (2.3) and the fifth (4.2), while for the points 2.4, 1.2, 5.8, 3.2, 7.1, there are three local maxima. (a) What is the probability that the fifth point is the only local maxima, namely that the sequence is increasing? (b) What is the expected number of local maxima