A European call option gives you the right but not the obligation to buy a stock for a

price K dollars (called the strike price) at time T (called the exercise time). Speculating

that the stock price will rise significantly, you paid a premium of C dollars today (at time

0) to buy the call option (think of this as buying a lottery ticket). Suppose the stock price

at time T, S, is a random variable with pdf f(s).

(a) What is the probability that the option is profitable?

(b) What is your expected payoff from the call option?