Reference no: EM13843763
1) On an exam there are 10 multiple choice questions. Each multiple choice question has four alternatives to choose from, of which only one is correct. A student can either be prepared or unprepared for the exam. Let us assume that it is equally likely for a student to be prepared or unprepared for the exam. If a student is prepared, then the student answers a question correctly with probability 0.9. On the other hand, if a student is unprepared, then the student answers a question correctly only with probability 0.25. Assume for simplicity that the correctness of the responses are independent across the questions. If a student has answered all 10 questions correctly, what is the probability that this student had prepared for the exam?
2) The stock price of company ABC tomorrow, X, can be modeled as a random variable which is normally distributed with a mean of INR 50 with a standard deviation of INR 10. Consider the following bet: If the stock price tomorrow (X) is greater than INR 55, then I will pay you the difference between the stock price X and INR 55. If the stock price tomorrow (X) is less than INR 45, then you will pay me the difference between 45 and the stock price X. If the stock price X is between 45 and 55, then there is no payment to either party.
a) Let Y denote your payoff from the bet. What is the functional relation between Y and X? That is, how does Y depend on X?
b) Write down a simulation model to estimate the expected payoff E(Y). Be sure to clearly state the different steps including the input random variable, its distribution, the output random variable and how to use the simulation to estimate the quantity of interest
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