# lec-18 - CS70 Satish Rao Administration 1 Midterm Exam...

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Unformatted text preview: CS70: Satish Rao: Administration. 1. Midterm Exam: October 10, 7-9, 155 Dwinelle. 2. Watch Piazza for extra office hours. Sunday: October 9th, 1-3 PM, 310 Soda. (Cook/Chan) Monday: October 10th. 10-11:30 AM, 687 Soda, Rao. Sunday: 3-6 PM, 310 Soda??? 3. No class on October 10. Study. CS70: Satish Rao: Lecture 18. 1. Probability Basics Review 2. Birthday Paradox. 3. Monty Hall 4. Conditional Probability. Probability. Setup: Probability. Setup: I Random Experiment. Probability. Setup: I Random Experiment. Flip a coin twice. Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Ω = { HH , HT , TH , TT } Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Ω = { HH , HT , TH , TT } I Probability: Pr [ ω ] for all ω ∈ Ω . Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Ω = { HH , HT , TH , TT } I Probability: Pr [ ω ] for all ω ∈ Ω . Pr [ HH ] = ··· = Pr [ TT ] = 1 / 4 Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Ω = { HH , HT , TH , TT } I Probability: Pr [ ω ] for all ω ∈ Ω . Pr [ HH ] = ··· = Pr [ TT ] = 1 / 4 1. ≤ Pr [ ω ] ≤ 1 . Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Ω = { HH , HT , TH , TT } I Probability: Pr [ ω ] for all ω ∈ Ω . Pr [ HH ] = ··· = Pr [ TT ] = 1 / 4 1. ≤ Pr [ ω ] ≤ 1 . 2. ∑ ω ∈ Ω Pr [ ω ] = 1 . Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Ω = { HH , HT , TH , TT } I Probability: Pr [ ω ] for all ω ∈ Ω . Pr [ HH ] = ··· = Pr [ TT ] = 1 / 4 1. ≤ Pr [ ω ] ≤ 1 . 2. ∑ ω ∈ Ω Pr [ ω ] = 1 . Definition: Event A ⊆ Ω , Pr [ A ] = ∑ ω ∈ Ω Pr [ ω ] . Probability. Setup: I Random Experiment. Flip a coin twice. I Probability Space. I Sample Space: Set of outcomes, Ω . Ω = { HH , HT , TH , TT } I Probability: Pr [ ω ] for all ω ∈ Ω . Pr [ HH ] = ··· = Pr [ TT ] = 1 / 4 1. ≤ Pr [ ω ] ≤ 1 . 2. ∑ ω ∈ Ω Pr [ ω ] = 1 . Definition: Event A ⊆ Ω , Pr [ A ] = ∑ ω ∈ Ω Pr [ ω ] . Event A : “exactly one heads”, A = { HT , TH } , Pr [ A ] = 1 2 Identity: A and A . Definition For an event A , the complement of A , A = Ω- A . A Ω A Identity: A and A ....
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lec-18 - CS70 Satish Rao Administration 1 Midterm Exam...

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