Handwritten solution for part a b c d

3.24 Some functions on the probability simpler. Let x be a real-valued random variable which takes values in {ai, ..., An} where ai a). (c) prob(a 0.25}. (g) The cardinality of the smallest set AC {a1, ..., an} with probability > 90%. (By cardinality we mean the number of elements in A.) (h) The minimum width interval that contains 90% of the probability, i.e., inf{B - a prob(a 0.9}