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 o.6 of increasing In any year. Moreover, the change in the Index n any given year ls 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) Xhas a binomial distribution. What are n and p? (b) What are the possible values that Xoan take? (Enter your answers as a comma-separated list.) (c) Find the probability of each value of x. Draw a probability histog for the distribution of x. (Enter your values for x from smallest to ram largest. Round your answers for the probabilities to four decimal places.) Probability (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.)

Explanation / Answer

a)n=5

p=0.6

b) x can take:0,1,2,3,4,5

c)

d) mean =np=5*0.6=3

std deviation =(np(1-p))1/2 =1.095

x P(x) 0 0.0102 1 0.0768 2 0.2304 3 0.3456 4 0.2592 5 0.0778

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