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Probability, Entropy, and MC Simulation
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The Central Limit Theorem is useful when the population distribution is unknown because it:
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To generate a variate from distribution F(x) using Inverse Transform method:
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In the analysis of the expected number of comparisons in QuickSort, the indicator random variable method relies on:
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Two discrete random variables X and Y are independent if and only if:
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The "information" or "surprise" I(x) of an event with probability p is:
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The first step in the Inverse Transform Method is to generate:
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A certain event (probability = 1) conveys:
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In the context of Conditional Expectation, E[Y | X = x] is:
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If X ~ Binomial(n, p) and Y ~ Binomial(m, p) are independent, what is the distribution of Z = X + Y?
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The correlation coefficient ρ between two random variables always satisfies:
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