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

A)   One.

B)   Zero.

C)   1/N.

D)   A random occurrence.

2、If a smooth curve is to represent a probability density function, what two requirements must be satisfied? The:

A)   area under the curve must be zero and the curve must not fall below the horizontal axis.

B)   area under the curve must be one and the curve must not rise above the horizontal axis.

C)   total area under the curve must be one and the curve must not fall below the horizontal axis.

D)   area under the curve must be zero and the curve must not rise above the horizontal axis.

3、Which of the following could NOT be a probability function?

A)   X1,2,3,4) p(x)= x/10.

B)   X1,2,3,4) p(x)=(5-x)/10.

C)   X1,2,3,4) p(x)=(x*x)/30.

D)   X1,2,3,4) p(x)= 0.2.

4、A probability function:

A)   only applies to continuous distributions.

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

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

D)   is completely determined by its median and mode.

答案和详解如下：

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

A)   One.

B)   Zero.

C)   1/N.

D)   A random occurrence.

The correct answer was B)

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.

2、If a smooth curve is to represent a probability density function, what two requirements must be satisfied? The:

A)   area under the curve must be zero and the curve must not fall below the horizontal axis.

B)   area under the curve must be one and the curve must not rise above the horizontal axis.

C)   total area under the curve must be one and the curve must not fall below the horizontal axis.

D)   area under the curve must be zero and the curve must not rise above the horizontal axis.

The correct answer was C)

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).

3、Which of the following could NOT be a probability function?

A)   X1,2,3,4) p(x)= x/10.

B)   X1,2,3,4) p(x)=(5-x)/10.

C)   X1,2,3,4) p(x)=(x*x)/30.

D)   X1,2,3,4) p(x)= 0.2.

The correct answer was D)

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.

4、A probability function:

A)   only applies to continuous distributions.

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

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

D)   is completely determined by its median and mode.

The correct answer was B)

This is true by definition.