8007 Sample Questions Answers

The determinant of a matrix X is equal 2. Which of the following statements is true?

The fundamental theorem of analysis establishes a relation between

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

You invest $100 000 for 3 years at a continuously compounded rate of 3%. At the end of 3 years, you redeem the investment. Taxes of 22% are applied at the time of redemption. What is your approximate after-tax profit from the investment, rounded to $10?

In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

Consider the following distribution data for a random variable X: What is the mean and variance of X?

The natural logarithm of x is:

What can be said about observations of random variables that are i.i.d. a normally distributed?

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

Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

Which of the following statements is not correct?

What is the simplest form of this expression: log2(165/2)

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?

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

Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X ≤ 0 and Y ≤ 1.96 is approximately