How do I do e? A believer in the \"random walk\" theory of the behavior of stock

Question

How do I do e?

A believer in the "random walk" theory of the behavior of stock prices 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 6 years in which the index rises. What are n and p in the binomial distribution of X? Give the possible values that X can take and the probability of each value. Draw a probability histogram for the distribution of X (Do this on paper. Your instructor may ask you to turn this in.) Find the mean of the number X of years in which the stock price index rises and mark the mean on your probability histogram Find the standard deviation of X What is the probability that X takes a value within one standard deviation of its mean?

Explanation / Answer

e) we have here X following a binomial distribution with n=6 and p=0.68

hence mean of X is E[X]=6*0.68=4.08 and variance of X is V[X]=6*0.68*(1-0.68)=1.3056

hence standard deviation of X is sqrt(1.3056)=1.142629

we need to find the probability of P[4.08-1.14*1<=X<=4.08+1.14*1] , the probability of X taking value within one standard deviation of mean.

so P[4.08-1.14*1<=X<=4.08+1.14*1]=P[2.94<=X<=5.22]=P[X=3]+P[X=4]+P[X=5]=0.20607+0.32842+0.27916=0.81365 [answer]

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