Question: A believer in the "random walk" theory of stock markets thinks that an index of stock prices has a probability of 0.65 of increasing in any given year. Moreover, she makes the assumption that the change in the index in any given year doesn't depend on whether the index rose or fell in previous years. Let X represent the number of years the index rises out of the next 5 years. The random variable X has a binomial distribution.
Construct a probability distribution for X, giving the values for X and the probabilities associated with them:
X
P(X)

What are the mean and standard deviation of this distribution?

What is the probability the index rises at least 2 years out of the 5 year period?