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
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,
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
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
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
86. The probability of obtaining at least two "SIX" in throwing a fair dice 4 times is
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
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?
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
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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