KP223 Lecture Notes - Lecture 6: Poisson Distribution, Central Limit Theorem, Statistical Parameter
12 Dec 2015
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Write x binomial(n, p) or x b(n, p). (cid:18)n (cid:19) x px (1 p)n x, for x = 0, 1, 2, . , n, p [0, 1: the pdf of x is given by p (x = x) , mean: x = np, variance: 2. , x = 0, 1, 2, : properties of simple random samples, a simple random sample is a set of random variables x1, x2, x3, . , xn which are independent and identically distributed (i. i. d: independent: Cov[xi, xj] = 0 for all i (cid:54)= j, i, j = 1, 2 . The {xi}"s all have the same p. d. f. (probability density function) as the parent random variable. The {xi}"s all have the same true mean e[x] and variance v [x] as the parent random variable x. Central limit theorem (6. 5. 2: consider a random sample of size n from a population with mean and standard deviation .
