4.5/10 points | Previous Answers MBasicStat7 14.E 025. A believer in the random

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4.5/10 points | Previous Answers MBasicStat7 14.E 025. A believer in the random walk theory of stock markets thinks that an index of stock prices has probability 0.52 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 My Notes Ask Your Teacher (a) X has a binomial distribution. What are n and p? . 0.52 (b) What are the possible values that X can take? (Enter your answers asa comma-separated list.) 0,1,2,3,4,5 (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.) Probability 0.0255 0.0107 (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.) 2.6 Vyeans x years standard deviation 1.250 eBook

Explanation / Answer

P(x) = 5Cx * 0.52x * (1-0.52)5-x

C) P(0) = 5C0 * 0.520 * 0.485 = 0.0255

P(1) = 5C1 * 0.521 * 0.484 = 0.1380

P(2) = 5C2 * 0.522 * 0.483 = 0.2990

P(3) = 5C3 * 0.523 * 0.482 = 0.3240

P(4) = 5C4 * 0.524 * 0.481 = 0.1755

P(5) = 5C5 * 0.525 * 0.480 = 0.0380

D) mean = n*p = 5 * 0.52 = 2.6

Standard deviation = sqrt (n*p*(1-p)) = sqrt(5*0.52*0.48) = 1.117

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