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1)What is meant by reversible process?
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2)What is meant by a stochastic process?
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3)The probabilities of occurrence of events F and G are P(F) = 0.3 and P(G) = 0.4, respectively. The probability that both events occur simultaneously is P(FG) = 0.2. The probability of occurrence of at least one event P(FG) is _______
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4)T he arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).
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5)L et X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) is
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6)Let X1;X2;X3;X4 be independent exponential random variables with mean 1; 1=2; 1=3; 1=4; respectively. Then Y = min(X1;X2;X3;X4) has exponential distribution with mean equal to .
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7)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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8)T he probability that a bush has a cricket is 0.1. The probability of a spider being present on a bush is 0.2. When both a spider and a cricket are present on a bush, the probability of encountering each other is 0.2. The probability of a spider consuming a cricket it encounters is 0.5. Assuming that predation only occurs on bushes, the probability that a cricket is preyed on by a spider is ____ (answer up to 3 decimal places).
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9)L et 1 X , 2 X , 3 X and 4 X be independent normal random variables with zero mean and unit variance. The probability that 4 X is the smallest among the four is _______.
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10)What is stochastic gradient descent ?
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