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Free Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Practice Questions

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Total Questions : 132

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Question # 11

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?

Options:

A.  

0.7367

B.  

0.3483

C.  

0.2646

D.  

None of these

Discussion 0
Question # 12

What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?

Options:

A.  

90 degrees

B.  

180 degrees

C.  

57 degrees

D.  

45 degrees

Discussion 0
Question # 13

A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5. What is the explained sum of squares?

Options:

A.  

0.75

B.  

1.125

C.  

0.3333

D.  

0.375

Discussion 0
Question # 14

In a multiple linear regression, the significance of R2 can be tested using which distribution?

Options:

A.  

Normal distribution

B.  

Student's t distribution

C.  

F-distribution

D.  

Binomial distribution

Discussion 0
Question # 15

Calculate the determinant of the following matrix:

Options:

A.  

4.25

B.  

-4.25

C.  

4

D.  

2

Discussion 0
Question # 16

Two vectors are orthogonal when:

Options:

A.  

one is a scalar multiple of the other

B.  

their components are linearly dependent

C.  

their determinant is zero

D.  

their scalar product (sum product) is zero

Discussion 0
Question # 17

Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

Options:

A.  

36%

B.  

36.33%

C.  

26.33%

D.  

20.78%

Discussion 0
Question # 18

The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

Options:

A.  

1

B.  

0.5

C.  

0

D.  

None of the above

Discussion 0
Question # 19

What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x ≤ 1, y ≥ -2, y-x ≤ 3 ?

Options:

A.  

29

B.  

-25

C.  

1

D.  

17

Discussion 0

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