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  4. 8007 - Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

8007 Exam Dumps - Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

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Question # 4

For each of the following functions, indicate whether its graph is concave or convex:

Y = 7x2 + 3x + 9

Y = 6 ln(3x)

Y = exp(-4x)

A.

concave, concave, concave

B.

concave, convex, convex

C.

convex, concave, concave

D.

convex, convex, concave

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Question # 5

A 95% confidence interval for a parameter estimate can be interpreted as follows:

A.

The probability that the real value of the parameter is within this interval is 95%.

B.

The probability that the real value of the parameter is outside this interval is 95%.

C.

The probability that the estimated value of the parameter is within this interval is 95%.

D.

The probability that the estimated value of the parameter is outside this interval is 95%.

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Question # 6

There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds. Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?

A.

0.3

B.

0.5

C.

0.6

D.

None of these

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Question # 7

What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,…?

A.

1 048 574

B.

1 048 595

C.

2 097 170

D.

2 097 172

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Question # 8

Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

A.

E(exp(X)) = 1.6487

B.

E(exp(X)) = 1

C.

E(exp(X)) = 2.7183

D.

E(exp(X)) = 0.6065

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