IntroProbability-4

# IntroProbability-4 - Sample Spaces Sample space S is set of...

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1 Sample Spaces Sample space , S, is set of all possible outcomes of an experiment Coin flip: S = {Head, Tails} Flipping two coins: S = {(H, H), (H, T), (T, H), (T, T)} Roll of 6-sided die: S = {1, 2, 3, 4, 5, 6} # emails in a day: S = { x | x Z, x ≥ 0} (non-neg. ints) YouTube hrs. in day: S = { x | x R , 0 x 24} Events Event , E, is some subset of S (E S) Coin flip is heads: E = {Head} ≥ 1 head on 2 coin flips: E = {(H, H), (H, T), (T, H)} Roll of die is 3 or less: E = {1, 2, 3} # emails in a day 20: E = { x | x Z , 0 x 20} Wasted day (>5 YT hrs.): E = { x | x R , x > 5} Note: When Ross uses: , he really means: Set operations on Events E F S Say E and F are events in S Say E and F are events in S S = {1, 2, 3, 4, 5, 6} die roll outcome E = {1, 2} F = {2, 3} E F = {1, 2, 3} Set operations on Events E F S E F Event that is in E or F

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2 Say E and F are events in S S = {1, 2, 3, 4, 5, 6} die roll outcome E = {1, 2} F = {2, 3} E F = {2} Note: mutually exclusive events means E F = Set operations on Events E F S E F or EF Event that is in E and F Say E and F are events in S S = {1, 2, 3, 4, 5, 6} die roll outcome E = {1, 2} E c = {3, 4, 5, 6} Set operations on Events E F S E c or ~E Event that is not in E (called complement of E) Say E and F are events in S Set operations on Events E F S (E F) c = E c F c DeMorgan’s Laws E F S (E F) c = E c F c n i c i c n i i E E 1 1 n i c i c n i i E E 1 1 Probability as relative frequency of event: Axiom 1: 0 P(E) 1
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IntroProbability-4 - Sample Spaces Sample space S is set of...

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