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An indefinite integral of a polynomial function is
What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?
An option has value 10 when the underlying price is 99 and value 9.5 when the underlying price is 101. Approximate the value of the option delta using a first order central finite difference.
Which of the following is consistent with the definition of a Type I error?
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?
Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?
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
Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter
Evaluate the derivative of ln(1+ x2) at the point x = 1
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?
An asset price S is lognormally distributed if:
Which of the following statements is true?
Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y
Which of the following statements is true for symmetric positive definite matrices?
Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24
A quadratic form is
Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1
Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%, +3%, -3%, +9%, -9% .
What can you say about the annual geometric and arithmetic mean returns of this investment fund?
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]?