Question 1

Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?

Question 2

Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

Question 3

Which of the following properties is exhibited by multiplication, but not by addition?

Question 4

What is the 40th term in the following series: 4, 14, 30, 52, …?

Question 5

In a quadratic Taylor approximation, a function is approximated by:

Question 6

What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,…?

Question 7

The sum of the infinite series 1+1/2+1/3+1/4+1/5+.... equals:

Question 8

Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?

Question 9

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is

Question 10

A linear regression gives the following output:

Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

Question 11

Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?

Question 12

Which of the following statements about variance and standard deviation are correct?

1. When calculated based on a sample of the population data, one has to correct for any bias in the result by using the number of degrees of freedom in the calculation

2. Variance is in square root units of the underlying data, whereas standard deviation is in units of the underlying data

3. When considering independent variables, variance is additive, while standard deviation is not

Question 13

Let f(x) = c for x in [0,4] and 0 for other values of x.

What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in [0,4]?

Question 14

A linear regression gives the following output:

Figures in square brackets are estimated standard errors of the coefficient estimates.

What is the value of the test statistic for the hypothesis that the coefficient of is less than 1?

Question 15

Evaluate the derivative of ln(1+ x2) at the point x = 1

Question 16

Which of the following statements is true for symmetric positive definite matrices?

Question 17

Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X. Assuming X is a normally distributed variable, what is Kurtosis(X)?

Question 18

A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

Question 19

For a quadratic equation, which of the following is FALSE?