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Теорія ймовірностей (ІП-41-43)

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

f(x) = [ (3 / 8) * x^2 , 0 < x <= 2; 0, otherwise ].

Which of the following is the median of X?

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

f(x) = [ 4* (x – x^3), 0 <= x <= 1; 0, otherwise ].

What is the mode of X?

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Given a continuous random variable X with probability density function f defined as follows:

f(x) = [ 5 / x^2 , x > 5; 0, otherwise ].

What is the mode of X?

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The continuous random variable X has a p.d.f. f(x) = [ 2 x, 0 <= x <= 1; 0, otherwise ]. Which of the following is true?

i. Var(X) = 1/18

ii. σ(X) = sqrt(2)/6

iii. Var(5X + 7) = 7 5/18

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

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

What is the standard deviation of X?

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Given a continuous random variable X with probability density function f defined as follows:

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

What is the mode of X?

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A random variable X has the probability density function given by

f(x) = [ 0.25, 0 <= x <= 4; 0, otherwise ]

What is mean?

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

f(y) = [ (3/256)* (16 – y^2), - 4 <= y <= 4; 0, otherwise ].

What is the standard deviation of Y?

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

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

Which of the following is the lower quartile of X?

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A random variable X has the probability density function given by f(x) = [ k * x^2 / 6 , -3 <= x <= 3 ; 0, otherwise ]

What is P(|X| < 1)

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