Reading 9: Common Probability Distributions LOS c习题精选 function, style, border, face

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LOS c: Interpret a probability function, a probability density function, and a cumulative distribution function.

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.

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This is true by definition.

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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.

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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.

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

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

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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).

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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.

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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.