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Lecture 9 Probability

# Lecture 9 Probability - Random Variables and Probability...

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Random Variables and Probability Pr(X = x) = p(x) The probability that a randomly selected element from a discrete distribution { X } will equal some given value, x : 0 Pr(X = x) 1 Pr(X = x) = 1 1

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Expected Value and Variance E(X) = x i Pr(X = x i ) Var(X) = E(X - μ) 2 = (x i - μ) 2 Pr(X = x i ) If X is a discrete random variable, then: 2
The Probability of an Event The probability that an event, A , will occur: Pr(A) = p The probability that an event other than A will occur, i.e. , the probability of not A : Pr(A’) = q 0 Pr(A) 1 Pr(A) + Pr(A’) = p + q = 1 3

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Independence and Intersections If two events, A and B , are independent, then the probability the both A and B will occur is: Pr(A B) = Pr(A)Pr(B) Two events are said to be independent if the occurrence of one event makes it neither more nor less probable that the other will occur 4
Unions and Mutual Exclusivity The probability that either event A , or event B , or both will occur: Pr(A B) = Pr(A) + Pr(B) - Pr(A B) Two events are said to be mutually exclusive if they cannot occur at the same time The union of two mutually exclusive events, A and B : Pr(A B) = Pr(A) + Pr(B) 5

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The probability that an event, A , will occur given that some other event, B , has already occurred ( i.e., the probability of A given B) : Pr(A | B) = Pr(A B) Pr(B) Pr(A B) = Pr(A
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Lecture 9 Probability - Random Variables and Probability...

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