Probability And Statistics - Study Mode

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[#66] The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is

(A) 0.25

(B) 0.33

(C) 0.50

(D) 0

Correct Answer

(A) 0.25

[#67] X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X - Y. The variance of Z is

(A) 0

(B) 1

(C) 2

(D) 3

Correct Answer

(D) 3

[#68] A hydraulic structure has four gates which operate independently. The probability of failure of each gate is 0.2. Given that gate 1 has failed, the probability that both gates 2 and 3 will fail is

(A) 0.240

(B) 0.200

(C) 0.040

(D) 0.008

Correct Answer

(C) 0.040

[#69] A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is

(A) $$frac{2}{{36}}$$

(B) $$frac{2}{6}$$

(C) $$frac{5}{{12}}$$

(D) $$frac{1}{2}$$

Correct Answer

(C) $$frac{5}{{12}}$$

[#70] Consider the finite sequence of random values X = [x 1 , x 2 , ... , x n ]. Let μ x be the mean and σ x be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as y i = a ∗ x i + b, where a and b are positive constant. Let μ y be the mean and σ y be the standard deviation of this sequence. Which one of the following statements INCORRECT?

(A) Index position of mode of X in X is the same as the index position of mode of Y in Y

(B) Index position of median of X in X is the same as the index position of median of Y in Y

(C) μ y = aμ x + b

(D) σ y = aσ x + b

Correct Answer

(D) σ y = aσ x + b