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Unformatted text preview: 68 CHAPTER 4. DISCRETE RANDOM VARIABLES Formula 4.3: Hypergeometric X ∼ H ( r , b , n ) X = the number of items from the group of interest that are in the chosen sample. X may take on the values x = 0, 1, ..., up to the size of the group of interest. (The minimum value for X may be larger than 0 in some instances.) r = the size of the group of interest (first group) b = the size of the second group n = the size of the chosen sample. n ≤ r + b The mean is: μ = nr r + b The standard deviation is: σ = r rbn ( r + b + n ) ( r + b ) 2 ( r + b- 1 ) Formula 4.4: Poisson X ∼ P( μ ) X = the number of occurrences in the interval of interest X takes on the values x = 0, 1, 2, 3, ... The mean μ is typically given. ( λ is often used as the mean instead of μ .) When the Poisson is used to approximate the binomial, we use the binomial mean μ = np . n is the binomial number of trials. p = the probability of a success for each trial. This formula is valid when n is "large" and p "small" (a general rule is that n should be greater than or equal to 20 and p should be less than or equal to 0.05). If n is large enough and p is small enough then the Poisson approximates the binomial very well. The standard deviation isbinomial very well....
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- Fall '08
- Statistics, Probability theory, Hypergeometric