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Midterm_Review

Midterm_Review - 2010 Spring PSTAT 120A Midterm Review...

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2010 Spring PSTAT 120A Midterm Review Sheet Series Review; The following are good exercises to review series knowledge. To verify probability mass functions of Binomial(n,p), Poisson( λ ), Geometry(p); Binomial(n,p): n X k =0 n k p k (1 - p ) n - k = 1 . Poisson( λ ): X k =0 λ k e - λ k ! = 1 . Geo(p): X k =1 p (1 - p ) k - 1 = 1 . To compute expectations: Binomial(n,p), Poisson( λ ),Geometry(p); Variance as well; * Binomial(n,p): n X k =0 k n k p k (1 - p ) n - k = np. * Poisson( λ ): X k =0 k λ k e - λ k ! = λ. * Geo(p): X k =1 kp (1 - p ) k - 1 = 1 p . 1 Combinatorics The first thing you should understand is the difference between with replacement and without replacement. Some problems explicitly say this, and some problems do not where you have to understand if replacement is allowed or not. E.g: birthday problem 2.48. Because different people can be born in the same months (so the denominator is 12 20 , that is, replacement is allowed). And problem 2.45( part b will be discussed later in Geometric distribution).

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Midterm_Review - 2010 Spring PSTAT 120A Midterm Review...

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