2 The behaviour of a certain stock market index is considered over the next (n+1) consecutive trading days starting from tomorrow. For each day a +' will be recorded if the index rises above the previous day's index and a -' will be recorded otherwise (you may assume that the probability that the index will be the same on two consecutive days is zero). Assume that rises and falls are independent and equally likely and that today's index exceeds yesterday's index. (a) Let N be the number of days of the next n for which a +' will be recorded. (i) Is N a binomial random variable? Justify your answer. (ii) What are the mean and standard deviation of N? (iii) Determine the probability that rises outnumber falls over the next 5 days.

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.