PRMIA 8007 Quiz 1 Topic 1 Questions 1-5

Question: 1

The gradient of a smooth function is

Aa vector that shows the direction of fastest change of a function

Bmatrix of second partial derivatives of a function

Cinfinite at a maximum point

Da matrix containing the function's second partial derivatives

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Question: 2

Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is

Amean is 0, variance is 2/3

Bmean is 0, variance is 1/3

Cmean is 0, variance is 1/2

Dmean is 1/3, variance is 1/3

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Question: 3

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:

A0.40729

B0.00109

C0.00087

D0.32583

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Question: 4

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?

Ab=0.5, a=2.5

Bb=0.5, a=1.5

Cb=2, a=4

Db=2, a=0

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Question: 5

In statistical hypothesis tests, 'Type I error' refers to the situation in which...

AThe null hypothesis is accepted when in fact it should have been rejected

BThe null hypothesis is rejected when in fact it should have been accepted

CBoth null hypothesis and alternative hypothesis are rejected

DBoth null hypothesis and alternative hypothesis are accepted

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PRMIA 8007 Quiz:1 Topic:1 Questions:1-5