A believer in the random walk theory of stock markets thinks that an index of st

Question

A believer in the random walk theory of stock markets thinks that an index of stock prices has probability 0.68 of increasing in any year. Moreover, the change in the index in any given year is not influenced by whether it rose or fell in earlier years. Let X be the number of years among the next five years in which the index rises. (a) X has a binomial distribution. What are n and p? n = p = (b) What are the possible values that X can take? (Enter your answers as a comma-separated list.) (c) Find the probability of each value of X. Draw a probability histogram for the distribution of X. (Enter your values for X from smallest to largest. Round your answers for the probabilities to four decimal places.) (d) What are the mean and standard deviation of this distribution? Mark the location of the mean on your histogram. (Round your answers to three decimal places.) mean years standard deviation years

Explanation / Answer

Par t a )

n = 5

p = 0.68

Part b)

X = 0,1,2,3,4 and 5

Part c)

x

formula

Probability

0

C(5,0) * 0.68^0 * 0.32^5

0.0034

1

C(5,1) * 0.68^1 * 0.32^4

0.0357

2

C(5,2) * 0.68^2 * 0.32^3

0.1515

3

C(5,3) * 0.68^3 * 0.32^2

0.3220

4

C(5,4) * 0.68^4 * 0.32^1

0.3421

5

C(5,5) * 0.68^5 * 0.32^0

0.1454

Part d)

mean = 5*0.68 = 3.400

standard deviation = sqrt (5*0.68*(1-0.68)) = 1.043

x

formula

Probability

0

C(5,0) * 0.68^0 * 0.32^5

0.0034

1

C(5,1) * 0.68^1 * 0.32^4

0.0357

2

C(5,2) * 0.68^2 * 0.32^3

0.1515

3

C(5,3) * 0.68^3 * 0.32^2

0.3220

4

C(5,4) * 0.68^4 * 0.32^1

0.3421

5

C(5,5) * 0.68^5 * 0.32^0

0.1454

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