Q1. A probability function:

A)     is often referred to as the "cdf."

B)     specifies the probability that the random variable takes on a specific value.

C)     only applies to continuous distributions.

Q2. Which of the following could least likely be a probability function?

A)     X1,2,3,4) p(x) = (x × x) / 30.

B)     X1,2,3,4) p(x) = x / 10.

C)     X1,2,3,4) p(x) = 0.2.

Q3. If a smooth curve is to represent a probability density function, what two requirements must be satisfied? The area under the curve must be:

A)   one and the curve must not rise above the horizontal axis.

B)   one and the curve must not fall below the horizontal axis.

C)   zero and the curve must not fall below the horizontal axis.

Q4. In a continuous probability density function, the probability that any single value of a random variable occurs is equal to what?

A)   One.

B)   1/N.

C)   Zero.

答案和详解如下：

Q1. A probability function:

A)     is often referred to as the "cdf."

B)     specifies the probability that the random variable takes on a specific value.

C)     only applies to continuous distributions.

Correct answer is B)

This is true by definition.

Q2. Which of the following could least likely be a probability function?

A)     X1,2,3,4) p(x) = (x × x) / 30.

B)     X1,2,3,4) p(x) = x / 10.

C)     X1,2,3,4) p(x) = 0.2.

Correct answer is C)

In a probability function, the sum of the probabilities for all of the outcomes must equal one. Only one of the probability functions in these answers fails to sum to one.

Q3. If a smooth curve is to represent a probability density function, what two requirements must be satisfied? The area under the curve must be:

A)   one and the curve must not rise above the horizontal axis.

B)   one and the curve must not fall below the horizontal axis.

C)   zero and the curve must not fall below the horizontal axis.

Correct answer is B)

If a smooth curve is to represent a probability density function, the total area under the curve must be one (probability of all outcomes equals 1) and the curve must not fall below the horizontal axis (no outcome can have a negative chance of occurring).

Q4. In a continuous probability density function, the probability that any single value of a random variable occurs is equal to what?

A)   One.

B)   1/N.

C)   Zero.

Correct answer is C)

Since there are infinite potential outcomes in a continuous pdf, the probability of any single value of a random variable occurring is 1/infinity = 0.

Q6. 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)   0.167.

B)   0.001.

C)   0.200.

Correct answer is A)

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

Q7. The number of ships in the harbor is an example of what kind of variable?

A)   Discrete.

B)   Indiscrete.

C)   Continuous.

Correct answer is A)

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

Q8. Which of the following is a discrete random variable?

A)     The realized return on a corporate bond.

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

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

Correct answer is C)

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.

Q9. Which of the following statements about probability distributions is most accurate?

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

B)   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.

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

Correct answer is B)

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.

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