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81
A point is randomly selected with uniform probability in the X-Y. plane within the rectangle with corners at (0, 0), (1, 0), (1, 2) and (0, 2). If P is the length of the position vector of the point, the expected value of p2 is
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Answer: Option D
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82
Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2 respectively. Consider Y = X1 - X2; μ1 = μ2 = 1, σ1 = 1, σ2 = 2, Then,
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Answer: Option B
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83
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is μ. The standard deviation for this distribution is given by
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Answer: Option A
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84
Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $$\frac{1}{2}$$, the values of $${\text{P}}\left( {\frac{{\text{A}}}{{\text{B}}}} \right)$$  and $${\text{P}}\left( {\frac{{\text{B}}}{{\text{A}}}} \right)$$  respectively are
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Answer: Option D
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85
An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is
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Answer: Option C
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86
The probability of obtaining at least two "SIX" in throwing a fair dice 4 times is
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Answer: Option B
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87
A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is
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Answer: Option B
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88
Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?
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Answer: Option A
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89
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
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Answer: Option A
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90
X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X - Y. The variance of Z is
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Answer: Option D
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