04_03 - proof. p. 4-21 Summary for X ~ Binomial(n, p)...

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p. 4-21 proof . p. 4-22 Summary for X ~ Binomial( n , p ) Range: Pmf: Parameters: n {1, 2, 3, …} and 0 p 1 Mean: E ( X )= np Variance: Var ( X )= np (1 p ) X = { 0 , 1 , 2 ,...,n } f X ( x )= ¡ n x ¢ p x (1 p ) n x , for x X • Geometric and Negative Binomial Distributions Experiment: A basic experiment with sample space 0 is repeated infinite times. The sample space is = 0 × 0 × 0 × Assume that events depending on different trials are independent For a given event A 0 0 , we continue performing the trials until A 0 occurs exactly r times Q : What is the probability that we need to perform k trials?
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p. 4-23 Example. A company must hire 3 engineers. Each interview results in a hire with probability 1/3 Q : What is the probability that 10 interviews are required? We need: (i) 2 hires on the first 9 interview (ii) Success on the 10 th interview So, the probability is μ 9 2 ¶μ 1 3 2 μ 2 3 7 × μ 1 3 = μ 9 2 1 3 3 μ 2 3 7 .
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04_03 - proof. p. 4-21 Summary for X ~ Binomial(n, p)...

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