stock prices has a 0.6 probability of rising in any year. The change in the value of the index in any given year is not affected by whether it rose or fell in earlier years. You plan to record the value for the index in each of the next eight years. Let the random variable, X, represent the number of years (out of the next 8 years) in which the value of the index rises. a) If X is distributed according to the binomial probability distribution, what are the values for n and p?.. b) What are the possible values X can take, or equal? i QMETH 201, Homework 3 c) Calculate the probability X = 3
stock prices has a 0.6 probability of rising in any year. The change in the value of the index in any given year is not affected by whether it rose or fell in earlier years. You plan to record the value for the index in each of the next eight years. Let the random variable, X, represent the number of years (out of the next 8 years) in which the value of the index rises. a) If X is distributed according to the binomial probability distribution, what are the values for n and p?.. b) What are the possible values X can take, or equal? i QMETH 201, Homework 3 c) Calculate the probability X = 3
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:**Educational Exercise: Binomial Probability Distribution and Stock Market Analysis**
This exercise explores the application of the "random walk" theory in stock market analysis using the binomial probability distribution.
6) A believer in the "random walk" theory of stock markets believes that the value of an index of stock prices has a 0.6 probability of rising in any given year. The change in the index value for any given year is unaffected by changes in previous years. You plan to record the index value over the next eight years. Let the random variable \( X \) represent the number of years (out of the next 8 years) in which the index rises.
a) If \( X \) is distributed according to the binomial probability distribution, determine the values for \( n \) (the number of trials) and \( p \) (the probability of success on an individual trial).
b) Identify the possible values \( X \) can take.
**QMETH 201, Homework 3**
c) Calculate the probability that \( X = 3 \).
d) Calculate the expected value for \( X \).
e) Calculate the standard deviation for \( X \).
This exercise helps reinforce key statistical concepts and methods within the framework of financial markets, enhancing both theoretical understanding and practical application.
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