1、A random variable X is continuous and bounded between zero and five, X0≤X≤5). The cumulative distribution function (cdf) for X is F(x)=x/5. Calculate P(2≤X≤4).

A)   1.00.

B)   0.25.

C)   0.40.

D)   0.50.

2、Which of the following qualifies as a cumulative distribution function?

A)   F(1)=0.5, F(2)=0.25, F(3)=0.25.

B)   F(1)=0, F(2)=0.5, F(3)=0.5, F(4)=0.

C)   F(1)=0.3, F(2)=0.6, F(3)=0.3.

D)   F(1)=0, F(2)=0.25, F(3)=0.50, F(4)=1.

答案和详解如下：

1、A random variable X is continuous and bounded between zero and five, X0≤X≤5). The cumulative distribution function (cdf) for X is F(x)=x/5. Calculate P(2≤X≤4).

A)   1.00.

B)   0.25.

C)   0.40.

D)   0.50.

The correct answer was C)

For a continuous distribution, P(a≤X≤b) = F(b)-F(a). Here, F(4) = 0.8 and F(2) = 0.4. Note also that this is a uniform distribution over 0≤x≤5 so Prob(2<x<4) = (4-2)/5 = 40%

2、Which of the following qualifies as a cumulative distribution function?

A)   F(1)=0.5, F(2)=0.25, F(3)=0.25.

B)   F(1)=0, F(2)=0.5, F(3)=0.5, F(4)=0.

C)   F(1)=0.3, F(2)=0.6, F(3)=0.3.

D)   F(1)=0, F(2)=0.25, F(3)=0.50, F(4)=1.

The correct answer was D)

Because a cumulative probability function defines the probability that a random variable takes a value equal to or less than a given number, for successively larger numbers, the cumulative probability values must stay the same or increase.