Hi can someone help me answer these questions, and explain them to me please.

A believer in the random walk theory of stock markets thinks that an index of stock prices has probability 0.64 of increasing in any month. Moreover, the change in the index in any given month is not influenced by whether it rose or fell in earlier months. Let X be the number of months in the next year in which the index rises.

1. X has a binomial distribution. What are n and p? n=? p=?
2. What are the possible values that X can take? (Enter your answers as a comma-separated list with spaces between commas/entries.)
3. Find the probability of each value of X. (Round your answers for the probabilities to four decimal places.)

• P(X=0)
• P(X=1)
• P(X=2)
• P(X=3)
• P(X=4)
• P(X=5)
• P(X=6)
• P(X=7)
• P(X=8)
• P(X=9)
• P(X=10)
• P(X=11)
• P(X=12)

4) What are the theoretical mean and standard deviation of this distribution? (Round your answers to two decimal places.)

mean =

Standard deviation=

years