Question 1: I draw one stock at random from the following. All stocks are equally likely to be chosen.
500 stocks are Manufacturing stocks, of which 200 are small and 300 are large.
1000 stocks are Non-Manufacturing stocks, of which 600 are small and 400 are large.
Event A is the event that I draw a Manufacturing stock. Event B is the event that I draw a large stock.
Answer the following questions (1 point each)
i. How many possible outcomes are there in this experiment? Is each outcome equally likely?
ii. What is the probability of event B?
iii. What is the probability of event B AND A? What is the probability of B OR A occurring?
Today is Apr 29. GOOG will report earnings tomorrow, on Apr 30. AMZN will report earnings one week later. The probability that AMZN misses earnings (i.e., reports lower earnings than analysts expect) is 0.25. The probability that GOOG misses earnings is 0.20. The probability that AMZN misses earnings AND GOOG misses earnings is 0.1. One day passes, today is now Apr 30, and GOOG misses earnings. What is the probability now that AMZN misses earnings? Hint: there are two events, AMZN misses, and GOOG misses.
Elon Musk always buys a stock as soon as he has positive private information about that stock. But if he doesn’t have private information about a stock, he will buy that stock with a probability of 0.1. The probability that Musk has private information about a stock is 0.25. You see Elon Musk buy AMZN. What is the probability that he has private information about AMZN, given that he has traded? (Hint: this is about Bayes theorem. There are two events: a) Musk trades, and b) Musk has private information.)
I bet $100 on a horse A and $100 on horse B in separate races. On each horse, my expected dollar payoff (the money I expect to get back) is $60, and the standard deviation of my dollar payoff is $20. The two bets have no covariance. What is my expected total payoff? What is the standard deviation of my total payoff? (Hint: Suppose your dollar payoff on the first horse is a random variable X, and your dollar payoff on the second horse is Y. You know some rules about expected values and variances.)
A fund manager has twenty analysts working for her. Each analyst recommends a stock to the manager. The stock that any analyst picks has a 0.6 chance of beating the market. Assuming each analyst’s pick is independent of any other, what is the probability that 11 or more analyst picks beat the market?
I am teaching my ten year old daughter about the stock market. She “invests” $10 with me. I toss 2 coins. If both are tails, I pay her back $20. If one is heads and one is tails, I pay her back $5. If both are heads, I pay her nothing. What is her expected payoff? What is the variance of her payoff?
The MTA’s daily operating profit is normally distributed with a mean of -30 million dollars (that’s negative 30) and an SD of 50 million dollars. The new mayor of NYC needs to communicate this information to the public, and asks you to give her a range of daily revenues, which contain 90% of the possible values. Give her two numbers, a lower and upper bound, so that there’s a 5% chance that the daily revenue is less than the lower bound, and a 5% chance it is more than the upper bound.
Students who graduate from Tobin have average annual salaries that are approximately normally distributed with mean 60000 and SD XXXXXXXXXXTen of my students graduated last year, and I call them up and say “If you have a job paying more than 100,000, you’re taking me out to a lobster dinner.” What is the probability that AT LEAST one student says yes, and I get to eat lobster?
I invested the same amount, $100 in each of 50 stock picks. The average amount I made was $110, and the standard deviation of the amount I made was 45. Test the null hypothesis that I have no skill: i.e., the population mean of the amount I made back was $100. Make sure to state your conclusion about whether I have skill or not.