Suppose you are trying to model the price of wheat and notice that it rises above 4$ per bushel on average 6 times each year. Let T be the next time (in years) from now that the price of wheat rises above 4$. Assume T is exponentially distributed, so T is continuous with pdf f(t) = , 0 t

a. State the value of and compute the probability that the price of wheat rises above 4$ within the first 3 months

b. Compute the probability that the price of wheat first rises above 4$ after 6 months but before 12 months

c. Compute the probability that the price of wheat does not rise above 4$ until after 9 months. d. What is the expected time until the price rises above 4$?

e. What is the standard deviation?