Reading 9: Common Probability Distributions LOS d习题精选 interpret, function, following, 2010

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

Which of the following qualifies as a cumulative distribution function?

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

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

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.

honeycfa

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) 0.40.

B) 1.00.

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%.