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lec-24 - CS70 Satish Rao Lecture 24 1 Geometric...

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Unformatted text preview: CS70: Satish Rao: Lecture 24. 1. Geometric Distribution. 2. Coupon Collector: Expectation. 3. Poisson Distribution. Geometric Distribution. Flip a coin with heads probability p until you get heads. Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . i- 1 tails, 1 heads ... Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . i- 1 tails, 1 heads ... Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . i- 1 tails, 1 heads ... P [ X = i ] = Pr [ “first i- 1 flips tails” ] × Pr [ “last is heads” ] Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . i- 1 tails, 1 heads ... P [ X = i ] = Pr [ “first i- 1 flips tails” ] × Pr [ “last is heads” ] Pr [ X = i ] Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . i- 1 tails, 1 heads ... P [ X = i ] = Pr [ “first i- 1 flips tails” ] × Pr [ “last is heads” ] Pr [ X = i ] = ( 1- p ) Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . i- 1 tails, 1 heads ... P [ X = i ] = Pr [ “first i- 1 flips tails” ] × Pr [ “last is heads” ] Pr [ X = i ] = ( 1- p ) ( i- 1 ) Geometric Distribution. Flip a coin with heads probability p until you get heads. Ω = { H , TH , TTTH , TTTH ,... } X- number of flips until success. When X = i contains single outcome: TTT ··· H . i- 1 tails, 1 heads ... P [ X = i ] = Pr [ “first i- 1 flips tails” ] × Pr [ “last is heads” ] Pr [ X = i ] = ( 1- p ) ( i- 1 ) p Geometric Distribution....
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lec-24 - CS70 Satish Rao Lecture 24 1 Geometric...

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