Question: A believer in the "random walk" theory of stock markets thinks that an index of stock prices has probability of 0.65 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.

a. X has a binomial distribution. What are n and p?
b. What are the possible values that X can take?
c. Find the probability of each value of X? draw a probability histogram for the distribution of X
d. What are the mean and standard deviation of this distribution? Mark the location of the mean on the histogram
e. Could the normal distribution be used to calculate probabilities in this problem? Why or why not?