Stat400lec16 - Statistics 400 Lecture 16 Review Random Variable(R.V is a variable whose value is a numerical outcome of a random phenomenon

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Statistics 400 Lecture 16 Review Random Variable: (R.V.) is a variable whose value is a numerical outcome of a random phenomenon. Notation : X, Y, Z Probability Theorem 2.1-1 : Complementary Rule: P (A ) = 1-P (A) Theorem 2.1-2 : P( Φ )=0 Theorem 2.1-3: If B A , P(A) P(B) Theorem 2.1-5 : Addition Rule: P ( B A )=P(A) + P(B) - P( B A ) Conditional Probability: the probability of a certain event given that a specific condition is satisfied. Assume P (A) > 0 ) ( ) ( ) | ( B P B A P B A P = = ) ( ) ( B P AandB P Properties of conditional probability: (A) 1 P(A|B) 0 (B)P(B|B)=1 (C)If A1, A2, A3,…Ak are mutually exclusive events P(A1 A2 Ak|B)=P(A1|B)+P(A2|B)+…+P(Ak|B) Definition 2.3.2 P(A B)=P (A and B) = P(B|A) * P (A) P(A B)=P (A and B) = P(A|B) * P (B) Ping Ma Lecture 16 Fall 2005 - 1 -

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Event A and event B are independent if P(A B)=P(A and B) = P (A) * P (B) Bayes’ Theorem P(B|A)= ) ( ) ( A P A B P = ) B' | P(A * ) P(B' B)
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This note was uploaded on 07/24/2008 for the course STAT 400 taught by Professor Tba during the Fall '05 term at University of Illinois at Urbana–Champaign.

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Stat400lec16 - Statistics 400 Lecture 16 Review Random Variable(R.V is a variable whose value is a numerical outcome of a random phenomenon

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