1、A random variable that has a countable number of possible values is called a:

A)   discrete random variable.

B)   continuous random variable.

C)   probability distribution.

D)   binomial random variable.

2、Which of the following is least likely to be an example of a discrete random variable?

A)   Quoted stock prices on the NASDAQ.

B)   The rate of return on a real estate investment.

C)   The number of days of sunshine in the month of May 2006 in a particular city.

D)   The number of shareholders of General Electric common stock.

3、Assume a discrete distribution for the number of possible sunny days in Provo, Utah during the week of April 20 through April 26. For this discrete distribution, p(x) = 0 when x cannot occur, or p(x) > 0 if it can. Based on this information, what is the probability of it being sunny on 5 days and on 10 days during the week?

                 5 Days of Sunshine         10 Days of Sunshine

A)      A positive value                         Infinite

B)      Zero                                        Infinite

C)      A positive value                        Zero

D)      A negative value                       Zero

答案和详解如下：

1、A random variable that has a countable number of possible values is called a:

A)   discrete random variable.

B)   continuous random variable.

C)   probability distribution.

D)   binomial random variable.

The correct answer was A)

A discrete random variable is one for which the number of possible outcomes are countable, and for each possible outcome, there is a measurable and positive probability. A continuous random variable is one for which the number of outcomes is not countable.

2、Which of the following is least likely to be an example of a discrete random variable?

A)   Quoted stock prices on the NASDAQ.

B)   The rate of return on a real estate investment.

C)   The number of days of sunshine in the month of May 2006 in a particular city.

D)   The number of shareholders of General Electric common stock.

The correct answer was B)

The rate of return on a real estate investment, or any other investment, is an example of a continuous random variable because the possible outcomes of rates of return are infinite (e.g., 10.0%, 10.01%, 10.001%, etc.). All the other choices are measurable (countable).

3、Assume a discrete distribution for the number of possible sunny days in Provo, Utah during the week of April 20 through April 26. For this discrete distribution, p(x) = 0 when x cannot occur, or p(x) > 0 if it can. Based on this information, what is the probability of it being sunny on 5 days and on 10 days during the week?

                 5 Days of Sunshine         10 Days of Sunshine

A)      A positive value                         Infinite

B)      Zero                                        Infinite

C)      A positive value                        Zero

D)      A negative value                       Zero

The correct answer was C)

The probability of it being sunny on 5 days during the week has some positive value, but the probability of having sunshine 10 days within a week of 7 days is zero because this cannot occur.