aianjie

 

14、Dependent random variables are defined as variables where their joint probability is:

A) equal to zero.

B) greater than the product of their individual probabilities.

C) not equal to the product of their individual probabilities.

D) equal to the product of their individual probabilities.

aianjie

 

The correct answer is C

Dependence results between random variables when their joint probabilities are not equal products of individual probabilities. If they are equal, then an independent relationship exists.

aianjie

 

15、An investor is choosing one of twenty securities. Ten of the securities are stocks and ten are bonds. Four of the ten stocks were issued by utilities, the other six were issued by industrial firms. Two of the ten bonds were issued by utilities, the other eight were issued by industrial firms. If the investor chooses a security at random, the probability that it is a bond or a security issued by an industrial firm is:

A) 0.80.

B) 0.70.

C) 0.60.

D) 0.50.

aianjie

 

The correct answer is A

Let B represent the set of bonds and I the set of industrial firms. The desired probability is the probability of the union of sets B and I, P(B I). According to the theorems of probability, P(B I)=P(B)+P(I)-P(B∩I), where P(B) is the probability that a security is a bond=P(B)=10/20, P(I) is the probability that a security was issued by an industrial firm=P(I)=14/20, and P(B∩I) is the probability that a security is both a bond and issued by an industrial firm=P(B∩I)=8/20. 10/20+14/20-8/20=16/20=0.80.

aianjie

 

16、X and Y are discrete random variables. The probability that X = 3 is 0.20 and the probability that Y = 4 is 0.30. The probability of observing that X = 3 and Y = 4 concurrently is closest to:

A) 0.

B) Cannot answer with the information provided.

C) 0.06.

D) 0.50.

aianjie

 

The correct answer is B

If you knew that X and Y were independent, you could calculate the probability as 0.20(0.30) = 0.06. Without this knowledge, you would need the joint probability distribution.

aianjie

 

17、The probabilities that three students will earn an A on an exam are 0.20, 0.25, and 0.30, respectively. If each student’s performance is independent of that of the other two students, the probability that all three students will earn an A is closest to:

A) 0.0150.

B) 0.0075.

C) 0.0010.

D) 0.7500.

aianjie

 

The correct answer is A

Since the events are independent, the probability is obtained by multiplying the individual probabilities. Probability of three As = (0.20) × (0.25) × (0.30) = 0.0150.

aianjie

 

AIM 3: Explain the relative frequency or the empirical definition of probability.

1、

Return, R	Frequency
–10% up to 0%	3
0% up to 10%	7
10% up to 20%	3
20% up to 30%	2
30% up to 40%	1

The number of intervals in this frequency table is:

A)    5.

B)    1.

C)   16.

D)   50.

aianjie

 

The correct answer is A

An interval is the set of return values that an observation falls within. Simply count the return intervals on the table—there are 5 of them.

[此贴子已经被作者于2009-6-25 9:22:34编辑过]