![]() It describes the probability distribution of the number of successes when drawing n samples from a finite population of size N, containing exactly K successes. The hypergeometric distribution is described by the three parameters N, K and n. The result is Γ(N + 1)/Γ(k), where Γ is the gamma function see gamma(). In SpeedCrunch, the domain of npr() is extended to all real numbers. permutations of a subset are counted as an additional choice. The order of the k elements is important, i.e. npr ( N k ) ¶Ĭomputes the binomial coefficient, equal to the number of possibilities of how to select k elements from a set of size N. The result is 1/((N + 1) * B(k + 1, N - k + 1)), where B(a, b) is the complete Beta function. In SpeedCrunch the domain of ncr() is extended to all real numbers. permutations of a subset are not counted as an additional choice. The order of the k elements is of no importance, i.e. ncr ( N k ) ¶Ĭomputes the binomial coefficient, equal to the number of possibilities of how to select k elements from a set of size N. binomvar ( N p ) ¶Ĭomputes the variance of the given binomial distribution function, equal to N * p * (1-p). The result will simply be given by N * p. The function computes the expected number of successes when an experiment is performed N times, each successful independently with probability p. Mean (expectation) value of the given binomial distribution. The function computes the probability, that, for N independent repetitions of a test successful with probability p each, the total number of successes is less than or equal to x.Įxample: When tossing a fair coin 9 times, what is the probability that we find Heads at most 5 times?īinompmf ( 5 9 0.5 ) = 0.24609375 binommean ( N p ) ¶ p – probability to succeed a single trial, 0 N – number of trials, must be a positive integer.x – maximum number of successes, must be integer. ![]() binomcdf ( x N p ) ¶īinomial cumulative distribution function. The binomial distribution can be thought of drawing with replacement, while the hypergeometric distribution describes drawing without replacement. Not that unlike the Hypergeometric Distribution, the probability p remains the same for all draws. It gives the probability distribution of the number of successful trials, when the total number of trials is given by N, and each test is successful with probability p. ![]() The binomial distribution is described by the parameters N and p. The arguments must share the same dimension. The variance is measure for the spreading of a set of numbers. ) ¶Ĭomputes the population variance of the arguments. ) ¶Ĭomputes the product of all the given arguments. ) ¶Ĭomputes the sum of all the given arguments. The arguments must be real and share the same dimension. Returns the maximum out of the supplied argument list. Returns the minimum out of the supplied argument list. If the number of arguments is even, the arithmetic mean of the two central elements is returned. ![]() If the number of arguments is odd, the element in the middle of the sorted list is returned. the value dividing the set of arguments into two evenly sized parts.įirst the set of arguments is sorted. ) ¶Ĭomputes the median of the arguments, i.e. The geometric mean is useful for comparing sets of quantities that are very different in order of magnitude and even possibly dimension. All the arguments may each have a different dimension. )^(1/n) where n is the number of arguments. ) ¶Ĭomputes the geometric mean of the arguments, defined by product(x1 x2. Computes the arithmetic average of the arguments (sum of the arguments divided by their number). ![]()
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