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17 Cards in this Set
- Front
- Back
Union of two events |
p(E1∪E2) = p(E1) + p(E2) - p(E1∩E2) |
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Probability of E given F |
p(E|F) = p(E∩F)/p(F) |
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Baye's Theorm |
Given a partition {E1,E2,...} of a sample space:
p(Ei|F) = p(Ei∩F)/p(F) = p(F|Ei) p(Ei) / Σj p(F|Ej) p(Ej). |
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The events E and F are independent IFF |
p(E∩F) = p(E)p(F) |
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Probability of K success in N Bernoulli trials |
p = P(success) q = P(failure) |
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Binomial Distribution |
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Geometric Distribution number of trials until the first success. |
p ∈ (0,1] |
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Poisson distribution |
X ∼ P(λ) if ... λ - average number of events in given time interval. |
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Let X be a discrete random variable. Define the expected value of X |
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Expectation of geometric distribution. |
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Expectation of Binomial distribution |
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Expectation of Poisson distribution |
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General Var(X)= |
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Variance of Bernoulli trials |
Var(X)=pq |
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Variance of Geometric distribution |
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Variance of Binomial distribution |
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Variance of Poisson distribution |
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