|More problems can be found on the Chalk site for this course.
Sample problem #1
An automated random investment program can choose either stocks, bonds or currency futures, for short-term speculative investments. Stocks are selected with probability 50%, bonds with probability 30%, and currencies with probability 20%. During one quarter, stocks have a 30% chance of yielding any profit, bonds have 40% chance of being profitable, and currencies have a 70% chance of profit. Given that at the end of the quarter the investment program LOST on its automated selection, what is the probability that STOCKS were picked up by the program for investment?
Sample problem #2
A student entrepreneur examines the possibility of offering his classmates an insurance against getting a grade of C or below (“the critical grade”) in any of the 2 courses they intend to take next quarter. The probability of a random student to get a critical grade in any of the 2 courses is 0.2, and the events of getting such grade in the 2 course are independent of each other. The entrepreneur considers paying any student that buys such insurance 1.5 time the course tuition ($1000 per course) in case the student gets a critical grade in that course.
Find the (minimum) premium the entrepreneur should charge a typical a student in order to break even.
Sample problem #3
A stock trader is interested in studying the association between the price of a certain stock at the beginning of the quarter (the variable X) and its price at the end of the quarter (the variable Y). He wishes to run a linear regression model. He believes that such model is useful only if it is found that the estimated slope is greater than 1.
He collects data on the relevant prices for 50 consecutive quarters and finds that the estimated standard deviations of X and Y are S(X)=2, S(Y)=3, respectively.
(a) What should the minimal correlation coefficient between X and Y be for the model to be useful to the trader?
(b) In the regression analysis it is found that one quarter yielded a standardized residual of 3.74. The trader’s daughter, who is a graduate business student, tells her father that there is “an impressive probability that in the quarter pertaining to that residual, the market was unusually bullish.” Is she right? Explain in detail.