Q1. Consider an investment portfolio of $50,000 in stock A and $50,000 in stock B. The expected value of A is 9.5% and B is 6%. The variance of A is 13% and the variance of B is 8%. The covariance between A and B is 18.6%.
(a) Compute the portfolio's weights associated with stock A and stock B.
(b) Obtain the portfolio expected return.
(c) Find the variance of the portfolio.
Q2. Approximately 80% of workers are sure that they will be able to retire at 65 years of age. Suppose 10 workers are randomly selected.
(a) What is the probability that none of the workers will be able to retire at 65?
(b) What is the probability that 2 workers will retire at 65?
(c) Find the expected value, variance and standard deviation of the random variable X defined as ‘retirement at 65'.
Q3. In the U.S., it is estimated that an average person makes 4 visits a year to doctor's offices.
(a) What is the mean and standard deviation for an average person of the number of monthly visit to the doctor?
(b) What is the probability that an average person makes at least 1 monthly visit to the doctor?