8002 Exam Dumps - PRM Certification - Exam II: Mathematical Foundations of Risk Measurement
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
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)?
Which of the following properties is exhibited by multiplication, but not by addition?
Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.
You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is …
Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24
Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:
A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution
You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?
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?
You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?
Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?