[2008] Topic 4: Characteristics of Probability Distributions 相关习题 investment, interpret, acquired, expected, investor

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AIM 1: Define, calculate and interpret the expected value.

1、An investor is considering purchasing ACQ. There is a 30% probability that ACQ will be acquired in the next two months. If ACQ is acquired, there is a 40% probability of earning a 30% return on the investment and a 60% probability of earning 25%. If ACQ is not acquired, the expected return is 12%. What is the expected return on this investment?

A) 18.3%.

B) 16.5%.

C) 12.3%.

D) 17.4%.

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aianjie

The correct answer is B

Independent random variables have a covariance of zero. Hence, the variance of the sum of two variables will be the sum of the variables’ variances.

aianjie

The correct answer is C

p(X=1)=0.05+0.05+0.10=0.20, p(X=2)=0.05+0.10+0.15=0.30, and p(X=3)=0.15+0.15+0.20=.50. Thus, the mean of X is equal to μ=0.20(1)+0.30(2)+0.50(3)=2.3, and the variance is calculated as 0.20(1-2.3)2+0.30(2-2.3)2+0.50(3-2.3)2=0.61.

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3、The variance of the sum of two independent random variables is equal to the sum of their variances:

A) plus a positive covariance term.

B) plus zero.

C) minus a positive covariance term.

D) plus a non-zero covariance term.

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If you know that Y is equal to 2, the probability that X is equal to 1 is closest to:

A) 0.05.

B) 0.25.

C) 0.17.

D) 0.20.

aianjie

The correct answer is C

p(X=1|Y=2)=0.05/(0.05+0.10+0.15)=0.17.