Let X be a random variable with probability density function (60(1- 6x (1-r) if x = [0, 1], otherwise. The probability of the event ≤X ≤ 1 is 13 O O O 54 13 27 O 20 00 27 01 5

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A: The discrete random variable  and  with joint probability function is given by:

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A: Let X be a discrete random variable with probability mass function.

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Q: 8. (a) Let f(x) be the pdf of a random variable X. if-2 ≤ x < 0 if 0 < x < 1 x² - 4x + 4 if 1 ≤ x ≤…

A: Farmula used P(X≤x)=F(x)

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A: GivenP(a&lt;X≤b)

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A: It a and b are positive integers where a ≤ b and X is a random variable that takes values with equal…

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Q: Let X = (X₁, X2, X3, X₁)' have probability distribution function 20! f(11, 12, 13, 14) = #₁!₂!3!₁!…

A:

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Q: Question is attached, Thanks

A: It is given that the expected value of X of a discrete probability is equal to mean.Thus,

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Q: 4. Determine the values of c so that the following functions represent joint probability…

A: The question is about joint probability distribution.Given :

Q: 4. Determine the values of c so that the following functions represent joint probability…

A: The objective is to find the value of by representing each function as a joint probability…