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Unformatted text preview: Lecture No: 10 Sampling with replacement : If we choose randomly with replacement a sample of n objects from N objects of which r are favorable and X= number of favorable objects in the sample chosen, then X has binomial distribution with parameters n and p=r/N. Ex : From a usual pack of 52 cards, 10 cards are picked randomly with replacement. Find the probability that they will contain at least 4 and at most 7 spades. Identify Bernoulli trials and success and random variable X together with its distribution. n=10, p=0.25 . Required probability = F(7)F(3) = 0.9996 0.7759(By tables) Hyper geometric distribution If we are choosing without replacement a sample of size n from N objects of which r are favorable, and X =number of favorable objects in the sample, then otherwise. 0 and r) min(n, x r)] (N n max[0, if  = = ; n N x n r N x r ] x X [ P Properties: The experiment consists of drawing a random sample of size n without replacement and without regard to order from a collection of N objects. Of the N objects, r have a trait of interest to us; the other (Nr) do not have the trait The random variable X is the number of objects in the sample with the trait. DO not have trait (failure) (N r) Have trait (Success ) r N objects Select n General hyper geometric setting Definition...
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 Spring '10
 XYZ
 Math, Binomial

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