1、Which of the following statements about probability distributions is most accurate?

A)   A binomial distribution counts the number of successes that occur in a fixed number of independent trials that have mutually exclusive (i.e. yes or no) outcomes.

B)   A continuous uniform distribution has a lower limit but no upper limit.

C)   A cumulative distribution function defines the probability that a random variable is greater than a given value.

D)   A discrete uniform random variable has varying probabilities for each outcome that total to one.

2、Which of the following is a discrete random variable?

A)   The amount of time between two successive stock trades.

B)   The realized return on a corporate bond.

C)   The weight of debris swept off the floor of the NYSE in a day.

D)   The number of advancing stocks in the DJIA in a day.

3、The number of ships in the harbor is an example of what kind of variable?

A)   Discrete.

B)   Indiscrete.

C)   Continuous.

D)   Discontinuous.

4、A dealer in a casino has rolled a five on a single die three times in a row. What is the probability of her rolling another five on the next roll, assuming it is a fair die?

A)   0.001.

B)   0.500.

C)   0.200.

D)   0.167.

5、A probability distribution is least likely to:

A)   contain all the possible outcomes.

B)   have only non-negative probabilities.

C)   apply to continuous or discrete random variables.

D)   give the probability that the distribution is realistic.

答案和详解如下：

1、Which of the following statements about probability distributions is most accurate?

A)   A binomial distribution counts the number of successes that occur in a fixed number of independent trials that have mutually exclusive (i.e. yes or no) outcomes.

B)   A continuous uniform distribution has a lower limit but no upper limit.

C)   A cumulative distribution function defines the probability that a random variable is greater than a given value.

D)   A discrete uniform random variable has varying probabilities for each outcome that total to one.

The correct answer was A)    

Binomial probability distributions give the result of a single outcome and are used to study discrete random variables where you want to know the probability that an exact event will happen. A continuous uniform distribution has both an upper and a lower limit. A discrete uniform random variable has equal probabilities for each outcome. A cumulative distribution function defines the probability that a random variable is equal to or less than a given value.

2、Which of the following is a discrete random variable?

A)   The amount of time between two successive stock trades.

B)   The realized return on a corporate bond.

C)   The weight of debris swept off the floor of the NYSE in a day.

D)   The number of advancing stocks in the DJIA in a day.

The correct answer was D)

Since the DJIA consists of only 30 stocks, the answer associated with it would be a discrete random variable. Random variables measuring time, rates of return and weight will be continuous.

3、The number of ships in the harbor is an example of what kind of variable?

A)   Discrete.

B)   Indiscrete.

C)   Continuous.

D)   Discontinuous.

The correct answer was A)    

A discrete variable is one that is represented by finite units.

4、A dealer in a casino has rolled a five on a single die three times in a row. What is the probability of her rolling another five on the next roll, assuming it is a fair die?

A)   0.001.

B)   0.500.

C)   0.200.

D)   0.167.

The correct answer was D)

The probability of a value being rolled is 1/6 regardless of the previous value rolled.

5、A probability distribution is least likely to:

A)   contain all the possible outcomes.

B)   have only non-negative probabilities.

C)   apply to continuous or discrete random variables.

D)   give the probability that the distribution is realistic.

The correct answer was D)

The probability distribution may or may not reflect reality. But the probability distribution must list all possible outcomes, and it can apply to continuous random variables. Probabilities can only have non-negative values.