Chap 11 Sums of Independent Random Variables and Limit Theorem Ghahramani 3rd edition 2019/5/16.

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Presentation transcript:

Chap 11 Sums of Independent Random Variables and Limit Theorem Ghahramani 3rd edition 2019/5/16

Outline 11.1 Moment-generating functions 11.2 Sums of independent random variables 11.3 Markov and Chebyshev inequalities 11.4 Laws of large numbers 11.5 Central limit theorem

Skip 11.1 Moment-generating functions 11.2 Sum of independent random variables

11.3 Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

Markov and Chebyshev inequalities

11.4 Laws of large numbers

Laws of large numbers

Laws of large numbers

Laws of large numbers

Laws of large numbers

Laws of large numbers

Laws of large numbers

Laws of large numbers

Laws of large numbers

11.5 Central limit theorem

Central limit theorem

Central limit theorem

Central limit theorem

Central limit theorem