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Probability Rules: 1. Let A be any event, then 0 ≤ P(A) ≤ 1 2. If S is the Sample space, then P(S)=1 3. If A and B are disjoint sets, then P(A or B)= P(A)+ P(B) = P(A U B) 4. If A and B are not disjoint sets, then P(A U B)= [P(A)+ P(B)] - P(A ∩ B) 5. If A is a set, then P(AC) = 1- P(A) 6. If A and B are independent, then P(A ∩ B) = P(A)* P(B) 7. If A and B are independent, then P(A ∩ B) =[P(A)+ P(B)] - P(A U B) Equally Likely Outcomes: P(A) = (# of outcomes in A) ÷ (#of outcomes in S) Conditional Probability: P(B│A)=P(A ∩ B)/P(A) & P(A│B)=P(A ∩ B)/ P(B) Independent: P(B│B) = P(A) & P(A│B)= P(A) To calculated Expected Value/Variance: (Discrete) m = å X i Pi x
i=1 ¥ X 2 s x = å ( X i - m) 2 P i x i=1 k
Note: Square Root of Variance is Standard Deviation
¥
(Continuous) m = ò X i f ( X i )dx x
-¥
s = ò ( X - m) 2 f ( x) dx x
2 x -¥
Linear Transformation: Xnew = a+ bX Mean: If X is a random variable and a and b are fixed numbers: m+bX = a + bm a x If X and Y are random variables:...

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