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Unformatted text preview: Administration I have regraded midterms. Come get them after class. Joke. Joke. Why do computer scientists confuse Halloween and Christmas? Joke. Why do computer scientists confuse Halloween and Christmas? OCT 31 = DEC 25 . Joke. Why do computer scientists confuse Halloween and Christmas? OCT 31 = DEC 25 . , CS70: Satish Rao: Lecture 28. 1. Polling. 2. Law of Large Numbers. 3. Joint Distributions Tail Bounds. Markov: For a non-negative random variable X , Pr [ X ≥ c ] ≤ E ( X ) c . Tail Bounds. Markov: For a non-negative random variable X , Pr [ X ≥ c ] ≤ E ( X ) c . Chebyshev’s Inequality: For a random variable X with expectation μ Pr [ | X- μ | ≥ α ] ≤ Var ( X ) α 2 . Tail bounds!!! Pr [ X ≥ i ] Chebyshev bound. Markov bound. . 5 1 . 15 30 45 60 75 90 105 120 135 150 Tail bounds!!! Pr [ | X- μ | ≥ i ] Chebyshev bound. Markov bound. . 5 1 . 15 30 45 60 75 90 105 120 135 150 Polling. Proportion of democrats? Polling. Proportion of democrats? Polling. Proportion of democrats? Poll: Choose a n people at random and average. Polling. Proportion of democrats? Poll: Choose a n people at random and average. How many people to get proportion within . 1 Polling. Proportion of democrats? Poll: Choose a n people at random and average. How many people to get proportion within . 1 with probability at least . 95? The setup. S n-number who are dems in sample. The setup. S n-number who are dems in sample. A n = 1 n S n . The setup. S n-number who are dems in sample. A n = 1 n S n . X i = 1 if i th person is democrat otherwise The setup. S n-number who are dems in sample. A n = 1 n S n . X i = 1 if i th person is democrat otherwise S n = ( X 1 + X 2 + ··· + X n ) . The setup. S n-number who are dems in sample. A n = 1 n S n . X i = 1 if i th person is democrat otherwise S n = ( X 1 + X 2 + ··· + X n ) . A n = 1 n S n . The setup. S n-number who are dems in sample. A n = 1 n S n . X i = 1 if i th person is democrat otherwise S n = ( X 1 + X 2 + ··· + X n ) . A n = 1 n S n . E ( A n ) = 1 n E ( S n ) The setup. S n-number who are dems in sample. A n = 1 n S n . X i = 1 if i th person is democrat otherwise S n = ( X 1 + X 2 + ··· + X n ) . A n = 1 n S n . E ( A n ) = 1 n E ( S n ) = 1 n ( pn ) = p . The setup. S n-number who are dems in sample. A n = 1 n S n . X i = 1 if i th person is democrat otherwise S n = ( X 1 + X 2 + ··· + X n ) . A n = 1 n S n . E ( A n ) = 1 n E ( S n ) = 1 n ( pn ) = p . The fraction of democrats! The setup. S n-number who are dems in sample. A n = 1 n S n . X i = 1 if i th person is democrat otherwise S n = ( X 1 + X 2 + ··· + X n ) . A n = 1 n S n . E ( A n ) = 1 n E ( S n ) = 1 n ( pn ) = p . The fraction of democrats! Unbiased estimator!!! The setup....
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