Questions from Calculus


Q: A random variable X has a cumulative distribution function F (x

A random variable X has a cumulative distribution function F (x) = 1/4 x2 on 0 ≤ x ≤ 2. Find b such that Pr (X ≤ b) = .09.

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Q: A random variable X has a cumulative distribution function F (x

A random variable X has a cumulative distribution function F (x) = (x - 1)2 on 1 ≤ x ≤ 2. Find b such that Pr (X ≤ b) = ¼.

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Q: Let X be a continuous random variable with values between A =

Let X be a continuous random variable with values between A = 1 and B = ∞, and with the density function f (x) = 4x-5. (a) Verify that f (x) is a probability density function for x ≥ 1. (b) Find the c...

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Q: Let X be a continuous random variable with the density function f

Let X be a continuous random variable with the density function f (x) = 2(x + 1)-3, x ≥ 0. (a) Verify that f (x) is a probability density function for x ≥ 0. (b) Find the cumulative distribution funct...

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Q: Verify that each of the following functions is a probability density function

Verify that each of the following functions is a probability density function. f (x) = 2(x - 1), 1 ≤ x ≤ 2

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Q: Verify that each of the following functions is a probability density function

Verify that each of the following functions is a probability density function. f (x) = ¼, 1 ≤ x ≤ 5

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Q: Verify that each of the following functions is a probability density function

Verify that each of the following functions is a probability density function. f (x) = 8/9 x, 0 ≤ x ≤ 3/2

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Q: Verify that each of the following functions is a probability density function

Verify that each of the following functions is a probability density function. f (x) = 5x4, 0 ≤ x ≤ 1

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Q: Verify that each of the following functions is a probability density function

Verify that each of the following functions is a probability density function. f (x) = 3/2 x – ¾ x2, 0 ≤ x ≤ 2

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Q: The annual incomes of the households in a certain community range between

The annual incomes of the households in a certain community range between 5 and 25 thousand dollars. Let X represent the annual income (in thousands of dollars) of a household chosen at random in this...

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