Math 203_Lecture 5

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

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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

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Review of two concepts Independence and mutually exclusive Principles of Statistics 1 Lecture 5: Math 203 – p. 2/4
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

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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
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

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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
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

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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
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

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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
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 . Principles of Statistics 1 Lecture 5: Math 203 – p. 5/4

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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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