Final Study Guide pt 2 - Quizzes

Question 1

How do you calculate the variance of a Bernoulli random variable?

Answer 1

(1 - E(X))^2 * p + (0 - E(X))^2 * (1-p)

Question 2

If a distribution is extremely skewed to the right, where will the mean appear in relation to the median?

Answer 2

To the right of the median

Question 3

An event has a probability of .02 of occurring.
Given 30 trial, what is the probability that it occurs a least once?

Answer 3

1 - Binomial(k = 0, n = 30,p = .02,Cumulative = F)

Question 4

Out of n trials, what is the probability that an event with probability p happens at least once?

Answer 4

1 - nC0 p^0 (1-p)^(n)

Question 5

Which of these turns a covariance matrix S into a correlation matrix C?

(/s) is side-by-side division. (Also known as element-wise division.)

(v) is a vector of the volatilities.

Answer 5

C = S (/s) (v * transpose(v))

Question 6

What is the equation for the variance of a portfolio of assets? w is an n-by-1 vector of asset weights

S is a covariance matrix for the returns of the assets.

Answer 6

transpose(w) S w

Question 7

What is the explained term in regression?

Answer 7

sum square (yhat - ybar)

Question 8

If the Duration is 10 and the present value of the bond $200, then if the rates go up 10% from 0%, then you will

Answer 8

lose $200

Question 9

If you know the sensitivity, you can get the elasticity by

Answer 9

multiplying the sensitivity by y/x

Question 10

SSR = Sum of Squared Residuals
SST = Sum of Squares Total
SSE = Sum of Explained Errors

What is the equation?

Answer 10

SST = SSE + SSR

Question 11

When the slope of a curve is zero, where the slope goes from negative, to zero, to positive, the point where the slope is zero is

Answer 11

a minimum

Question 12

At times, adjusted R-squared is used instead of R-squared in order

Answer 12

To compensate for adding variables to a regression model

Question 13

Which of these formulas represents an elastic response of y to x?

• dx/dy
• (dx/x)/(dy/y)
• dy/dx
• (dy/y)/(dx/x)

Answer 13

(dy/y)/(dx/x)

Question 14

What is the value of a slope beta when x does not affect y?

Answer 14

0

Question 15

What is d/dx 1000?

Answer 15

0

Question 16

What is a reasonable way to define Duration for an asset with cash flows CF over times t and a present value function PV?

Answer 16

D = Summation(t * PV(CF) / Summation(PV(CF))

Question 17

f’(x) = 0

Therefore

(Be careful here and also do not consider inflection points, as if they don’t exist)

Answer 17

f(x) is at a minimum

Question 18

What is d/dx (3x+1)^2?

Answer 18

(6)(3x + 1)

Question 19

On a two-tailed test with an alpha of .05, and a normal distribution where the sample data is 3 standard deviations away from the null hypothesis, we should reject the null hypothesis.

Answer 19

Yes, reject the null hypothesis

Question 20

When determining whether a distribution is the maximum likelihood, the reason to log the likelihood is because..

Answer 20

it handles the mechanical issue of multiplying extremely small numbers

Question 21

What is the likelihood of a data set?

Answer 21

The product of the probabilites of each point according to a distribution.

Question 22

ln(A x B x C) equals

Answer 22

ln(A) + ln(B) + ln(C)