Mutually Ex

# Mutually Ex - P(A n B = P(B/A)P(A = P(A/B)P(B P(B = P(B n A...

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Mutually Ex.: E1 n E2 = NULL PERMUTATIONS [ s = {a,b,c} perm = abc, acb, bac, bca,cab,cba = n! The number of Permutations of r elements selected from a set of n different elements = n! / (n-r)! The number of combinations … = n! / r!(n-r)! Order is not important For discrete sample space = P(E) = P(a) + P(b)+P(c) P(H U C) = P(H) + P(C) – P(H n C) Mutually exclusive = P(H U C) = P(H) + P(C) P(A U B U C) = P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C) The prob. of an event B under the knowledge that the outcome will be in A = P(B/A) P(B/A) = P(A n B) / P(A)
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Unformatted text preview: P(A n B) = P(B/A)P(A) = P(A/B)P(B) P(B) = P(B n A) + P(B n A’ ) = P(B/A)P(A) + P(B/A’ )P(A’ ) Independent if any one P(A/B) = P(A) P(B/A) =P(B) P(A n B) = P(A)P(B) Bayes Theorem = P(A n B) = P(A/B)P(B) = P(B n A)P(A) For P(B) > 0, P(A/B) = P(B/A)P(A) / P(B) Continuous: current, length, pressure, temperature, time, weight voltage Discrete: number of scratches, defected parts among 1000 Mean = u = E(X) = sum of x(f(x)) think of quiz 2. Variance = o^2 = V(X) = E(X – u)^2 = sum of (x – u)^2 * f(x) STD = sqrt(variance or o^2)...
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