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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. = { H , TH , TTTH , TTTH ,... } Geometric Distribution. Flip a coin with heads probability p until you get heads. = { H , TH , TTTH , TTTH ,... } X number of flips until success. Geometric Distribution. Flip a coin with heads probability p until you get heads. = { 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. = { 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. = { 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. = { 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. = { 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. = { 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. = { 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. = { 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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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.
 Fall '11
 Rau

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