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Теорія ймовірностей (ІП-41-43)

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A random variable Y has the p.d.f.

f(y) = [ (1/36)* (9 – y^2), - 3 <= y <= 3; 0, otherwise ].

What is the mean of Y?

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A random variable X has the p.d.f.

f(x) = [ 0, x < 0; x, 0 <= x <= 1; 2 – x , 1 <= x <= 2; 0, otherwise ].

What is the mean of X?

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A random variable Y has the p.d.f.

f(y) = [ (1/36)* (9 – y^2), - 3 <= y <= 3; 0, otherwise ].

What is the mode of Y?

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A random variable X has the p.d.f.

f(x) = [ (1/6)* (2 x + 1), 0 < x <= 2; 0, otherwise ].

Which of the following is the median of X?

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What is k for which the function below is a probability density function?

f(x) = [k / x^2, x > 10; 0, otherwise ]

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Function below is a probability density function f(x) = [3/5 + b*x^2 , 0 <= x <= 1 ; 0, otherwise ]

What is the P (X ≤ 0.5)?

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Which of the following is f(x) if F(x) = [ 0, x < 0; x^4, 0 < x < 1; 1, x > 1]?
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If f(x) = [ (2/9) * x; 0 <= x <= 3; 0, otherwise], then F(1) =
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The continuous random variable X has probability density function given by: f(x) = [ 2(3 - x), 2<= x <= 3; 0, otherwise ]

What is the P(2.5 < X < 3)?

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A continuous random variable X has density function f(x) = [ A (4 - x^2) , -2 <= x <= 2 ; 0, otherwise ]

What is A?

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