Question

Multiple Choice

Select the best answer from the available choices for each question.

1.   The return on stock X has mean 5 and standard deviation 3. The return on stock Y has mean 8 and standard deviation 10. The standard deviation of an equal portfolio of the two stocks (that is, 0.5X + 0.5Y) is 24.25. What is the correlation between X and Y?

•   -0.2
  
•   0

•   0.2

•   0.4
  
•   None of the above

2.     Suppose the length in cm of a male soccer player's foot follows a Normal distribution with mean 30 and variance 25. Suppose the length in cm of a female soccer player's foot follows a Normal distribution with mean 26 and variance 16. A male and female soccer player are selected at random. What is the probability the female player has a longer foot than the male player?

•   0.09

•   0.27

•   0.33

•   0.73

•   0.91

3.   Independently of one another, a randomly surveyed individual can be a non-smoker, a light smoker, or a heavy smoker with probabilities 60%, 30% and 10%, respectively. Suppose we randomly survey a sample of 100 people. Given that 37 of them are light smokers, what is the expected number of heavy smokers?

•   6.3

•   9

•   27

•   54

•   None of the above

4.   The Princess Theatre has 280 seats. 200 tickets are sold for the new popular movie: The Attack of the Goose. Despite every attendee having an assigned seat, they all decide to sit in seats at random. Find the variance of the number of people sitting in their assigned seat. (Hint: use indicator variables)

•   0.712

•   0.714

•   5.246

•   11.704

•   None of the above

Answer 1

1)

According to the question,

and,

Now,

Hence 1st option is the correct option.