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What are the conditions of the hypergeometric distribution?
The following conditions characterize the hypergeometric distribution: The result of each draw (the elements of the population being sampled) can be classified into one of two mutually exclusive categories (e.g. Pass/Fail or Employed/Unemployed). The probability of a success changes on each draw,…
How to calculate the sample size for hypergeometric?
Using the ( 1 − α / 2) quantile implies we want to conduct a two sided hypothesis test (otherwise we would have to use the ( 1 − α) quantile). Let’s use α = 0.01, i.e. an 99% confidence level. Now we get a result for sample size n: Clearly it is impractical to draw 2.6513 marbles from the urn.
Is the Fisher’s exact test based on the hypergeometric distribution?
The test based on the hypergeometric distribution (hypergeometric test) is identical to the corresponding one-tailed version of Fisher’s exact test. Reciprocally, the p-value of a two-sided Fisher’s exact test can be calculated as the sum of two appropriate hypergeometric tests (for more information see).
What is the formula for a generalized hypergeometric series?
A (generalized) hypergeometric series is a power series ∞ ∑ k = 0akxk where k ↦ ak + 1 /ak is a rational function (that is, a ratio of polynomials). Many of the basic power series studied in calculus are hypergeometric series, including the ordinary geometric series and the exponential series.
How to define conditional distributions for continuous variables?
That’s what we’ll do now! Suppose X and Y are continuous random variables with joint probability density function f ( x, y) and marginal probability density functions f X ( x) and f Y ( y), respectively. Then, the conditional probability density function of Y given X = x is defined as:
Is the probability of drawing green and red marbles exchangeable?
The probability of drawing any set of green and red marbles (the hypergeometric distribution) depends only on the numbers of green and red marbles, not on the order in which they appear; i.e., it is an exchangeable distribution.
Which is the binomial approximation to the hypergeometric?
The Binomial Approximation to the Hypergeometric Suppose we still have the population of size Nwith Munits labelled as “success” and N-Mlabelled as “failure,” but now we take a sample of size nis drawn with replacement. Then, with each draw, the units remaining to be drawn look the same: still M“successes” and N-M“failures.”