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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.

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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
Transcribed Image Text: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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