Q1. Which of the following statements about the normal probability distribution is most accurate?

A)   Sixty-eight percent of the area under the normal curve falls between 0 and +1 standard deviations above the mean.

B)   The normal curve is asymmetrical about its mean.

C)   Five percent of the normal curve probability falls more than outside two standard deviations from the mean.

Q2. Which of the following is least likely a probability distribution?

A)   Zeta Corp.: P(dividend increases) = 0.60, P(dividend decreases) = 0.30.

B)   Roll an irregular die: p(1) = p(2) = p(3) = p(4) = 0.2 and p(5) = p(6) = 0.1.

C)   Flip a coin: P(H) = P(T) = 0.5.

Q3. Which of the following statements about probability distributions is least accurate?

A)   A binomial probability distribution is an example of a continuous probability distribution.

B)   A discrete random variable is a variable that can assume only certain clearly separated values resulting from a count of some set of items.

C)   The skewness of a normal distribution is zero.

Q4. Which of the following statements about probability distributions is least accurate?

A)   A probability distribution is, by definition, normally distributed.

B)   In a binomial distribution each observation has only two possible outcomes that are mutually exclusive.

C)   A probability distribution includes a listing of all the possible outcomes of an experiment.

Q5. A probability distribution is least likely to:

A)     give the probability that the distribution is realistic.

B)     contain all the possible outcomes.

C)     have only non-negative probabilities.

答案和详解如下：

Q1. Which of the following statements about the normal probability distribution is most accurate?

A)   Sixty-eight percent of the area under the normal curve falls between 0 and +1 standard deviations above the mean.

B)   The normal curve is asymmetrical about its mean.

C)   Five percent of the normal curve probability falls more than outside two standard deviations from the mean.

Correct answer is C)

The normal curve is symmetrical with a mean of zero and a standard deviation of 1 with 34% of the area under the normal curve falling between 0 and +1 standard deviation above the mean. Ninety-five percent of the normal curve is within two standard deviations of the mean, so five percent of the normal curve falls outside two standard deviations from the mean.

Q2. Which of the following is least likely a probability distribution?

A)   Zeta Corp.: P(dividend increases) = 0.60, P(dividend decreases) = 0.30.

B)   Roll an irregular die: p(1) = p(2) = p(3) = p(4) = 0.2 and p(5) = p(6) = 0.1.

C)   Flip a coin: P(H) = P(T) = 0.5.

Correct answer is A)

All the probabilities must be listed. In the case of Zeta Corp. the probabilities do not sum to one.

Q3. Which of the following statements about probability distributions is least accurate?

A)   A binomial probability distribution is an example of a continuous probability distribution.

B)   A discrete random variable is a variable that can assume only certain clearly separated values resulting from a count of some set of items.

C)   The skewness of a normal distribution is zero.

Correct answer is A)

The binomial probability distribution is an example of a discrete probability distribution. There are only two possible outcomes of each trial and the outcomes are mutually exclusive. For example, in a coin toss the outcome is either heads or tails.

The other responses are both correct definitions.

Q4. Which of the following statements about probability distributions is least accurate?

A)   A probability distribution is, by definition, normally distributed.

B)   In a binomial distribution each observation has only two possible outcomes that are mutually exclusive.

C)   A probability distribution includes a listing of all the possible outcomes of an experiment.

Correct answer is A)

Probabilities must be zero or positive, but a probability distribution is not necessarily normally distributed. Binomial distributions are either successes or failures.

Q5. A probability distribution is least likely to:

A)     give the probability that the distribution is realistic.

B)     contain all the possible outcomes.

C)     have only non-negative probabilities.

Correct answer is A)

The probability distribution may or may not reflect reality. But the probability distribution must list all possible outcomes, and probabilities can only have non-negative values.

thank you

Q1. The covariance:

A)   must be between -1 and +1.

B)   can be positive or negative.

C)   must be positive.

Correct answer is B)         

Cov(a,b) = σ_aσ_bρ_a,b. Since ρ_a,b can be positive or negative, Cov(a,b) can be positive or negative.

Q2. With respect to the units each is measured in, which of the following is the most easily directly applicable measure of dispersion? The:

A)    covariance.

B)    variance.

C)    standard deviation.

Correct answer is C)

The standard deviation is in the units of the random variable itself and not squared units like the variance. The covariance would be measured in the product of two units of measure.

Q3. Personal Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Personal’s economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the covariance of the returns on Portfolio A and Portfolio B?

A)   0.890223.

B)   0.002019.

C)   0.001898.

Correct answer is C)

Q4. Given Cov(X,Y) = 1,000,000. What does this indicate about the relationship between X and Y?

A)  It is strong and positive.

B)  It is weak and positive.

C)  Only that it is positive.

Correct answer is C)

A positive covariance indicates a positive linear relationship but nothing else. The magnitude of the covariance by itself is not informative with respect to the strength of the relationship.

Q5. Which of the following statements is least accurate regarding covariance?

A)   Covariance can only apply to two variables at a time.

B)   Covariance can exceed one.

C)   A covariance of zero rules out any relationship.

Correct answer is C)

A covariance only measures the linear relationship. The covariance can be zero while a non-linear relationship exists. Both remaining statements are true.

a

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