Math 203_Lecture 5

Math 203_Lecture 5 - Principles of Statistics 1 Lecture 5...

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Unformatted text preview: Principles of Statistics 1 Lecture 5: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 09, 2011 Principles of Statistics 1 Lecture 5: Math 203 – p. 1/4 2 Review of two concepts Independence and mutually exclusive Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4 2 Review of two concepts Independence and mutually exclusive Two events A and B are independent if P ( A | B ) = P ( B ) or P ( B | A ) = P ( B ) or equivalently P ( A ∩ B ) = P ( A ) P ( B ) Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4 2 Review of two concepts Independence and mutually exclusive Two events A and B are independent if P ( A | B ) = P ( B ) or P ( B | A ) = P ( B ) or equivalently P ( A ∩ B ) = P ( A ) P ( B ) Two events A and B are mutually exclusive if A ∩ B = ∅ Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4 2 Review of two concepts Independence and mutually exclusive Two events A and B are independent if P ( A | B ) = P ( B ) or P ( B | A ) = P ( B ) or equivalently P ( A ∩ B ) = P ( A ) P ( B ) Two events A and B are mutually exclusive if A ∩ B = ∅ which implies P ( A ∩ B ) = 0 , and thus P ( A | B ) = 0 and P ( B | A ) = 0 . Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4 2 If A and B are mutually exclusive, then P ( A ∪ B ) = P ( A ) + P ( B ) . Principles of Statistics 1 Lecture 5: Math 203 – p. 3/4 2 Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4 2 Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft EXAMPLE : the experiment is rolling a six-sided fair die. A = { observing an odd number } B = { observing an even number } . Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4 2 Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft EXAMPLE : the experiment is rolling a six-sided fair die. A = { observing an odd number } B = { observing an even number } . Then A = { 1 , 3 , 5 } , B = { 2 , 4 , 6 } ⇒ A ∩ B = ∅ . Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4 2 Independence and mutually exclusive In general, the two concepts do not imply each other: Independence notarrowright mutually exclusive notarrowleft EXAMPLE : the experiment is rolling a six-sided fair die. A = { observing an odd number } B = { observing an even number } . Then A = { 1 , 3 , 5 } , B = { 2 , 4 , 6 } ⇒ A ∩ B = ∅ . A and B are mutually exclusive. But not independent: P ( A ) = 3 6 ,P ( B ) = 3 6 ⇒ P ( A ∩ B ) negationslash = P ( A ) P ( B ) Principles of Statistics 1 Lecture 5: Math 203 – p. 4/4 2 Example A stockbroker is researching 4 independent stocks. An investment in each stock will either make money or lose money. The probability that each stock will make money is 5/8 ....
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This note was uploaded on 07/15/2011 for the course MATH 203 taught by Professor Dr.josecorrea during the Summer '08 term at McGill.

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Math 203_Lecture 5 - Principles of Statistics 1 Lecture 5...

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