8007 Exam Dumps - Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)
A 95% confidence interval for a parameter estimate can be interpreted as follows:
There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds. Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?
What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,…?
Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?
When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?
A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points
Exploring a regression model for values of the independent variable that have not been observed is most accurately described as…
Find the first-order Taylor approximation p(x) for the function: at the point .
Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?
Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?
The Lagrangian of a constrained optimisation problem is given by L(x,y,λ) = 16x+8x2+4y-λ(4x+y-20), where λ is the Lagrange multiplier. What is the solution for x and y?
Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?
Which of the following statements concerning class intervals used for grouping of data is correct?
When grouping data, attention must be paid to the following with regards to class intervals:
1. Class intervals should not overlap
2. Class intervals should be of equal size unless there is a specific need to highlight data within a specific subgroup
3. The class intervals should be large enough so that they not obscure interesting variation within the group