Reading 9: Common Probability Distributions-LOS d 习题精选 2011, center, function, interpret

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Session 3: Quantitative Methods: Application
Reading 9: Common Probability Distributions

LOS d: Calculate and interpret probabilities for a random variable, given its cumulative distribution function.

 

 

A cumulative distribution function for a random variable X is given as follows:

x	F(x)
5	0.14
10	0.25
15	0.86
20	1.00

The probability of an outcome less than or equal to 10 is:

A) 14%.

B) 39%.

C) 25%.

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A cumulative distribution function (cdf) gives the probability of an outcome for a random variable less than or equal to a specific value. For the random variable X, the cdf for the outcome 10 is 0.25, which means there is a 25% probability that X will take a value less than or equal to 10.

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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) 0.40.

C) 0.50.

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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%.

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Which of the following qualifies as a cumulative distribution function?

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

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

C) F(1) = 0.5, F(2) = 0.25, F(3) = 0.25.

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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.