Questions from Calculus


Q: The density function for a continuous random variable X on the interval

The density function for a continuous random variable X on the interval 1 ≤ x ≤ 4 is f (x) = 4/9 x – 1/9 x2. (a) Use f (x) to compute Pr (3 ≤ X ≤ 4). (b) Find the corresponding cumulative distribution...

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Q: An experiment consists of selecting a point at random from the region

An experiment consists of selecting a point at random from the region inside the square in Fig. 10(a). Let X be the maximum of the coordinates of the point. Show that the cumulative distribution funct...

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Q: An experiment consists of selecting a point at random from the region

An experiment consists of selecting a point at random from the region inside the square in Fig. 10(a). Let X be the maximum of the coordinates of the point. Find the corresponding density function of...

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Q: An experiment consists of selecting a point at random from the region

An experiment consists of selecting a point at random from the region inside the triangle in Fig. 10(b). Let X be the sum of the coordinates of the point. Show that the cumulative distribution functio...

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Q: An experiment consists of selecting a point at random from the region

An experiment consists of selecting a point at random from the region inside the triangle in Fig. 10(b). Let X be the sum of the coordinates of the point. Find the corresponding density function of X....

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Q: In a certain cell population, cells divide every 10 days,

In a certain cell population, cells divide every 10 days, and the age of a cell selected at random is a random variable X with the density function f (x) = 2ke-kx, 0 ≤ x ≤ 10, k = (ln 2)/10. Find the...

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Q: In a certain cell population, cells divide every 10 days,

In a certain cell population, cells divide every 10 days, and the age of a cell selected at random is a random variable X with the density function f (x) = 2ke-kx, 0 ≤ x ≤ 10, k = (ln 2)/10. Upon exam...

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Q: A random variable X has a density function f (x)

A random variable X has a density function f (x) = 1/3, 0 ≤ x ≤ 3. Find b such that Pr (0 ≤ X ≤ b) = .6.

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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) = (x2 - 9)>16 on 3 ≤ x ≤ 5. (a) Find the density function for X. (b) Find a such that Pr (a ≤ X ) = ¼.

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Q: A random variable X has a density function f (x)

A random variable X has a density function f (x) = 2/3 x on 1 ≤ x ≤ 2. Find a such that Pr (a ≤ X ) = 13.

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