Probability: Binomial Distribution
Binomial Distribution The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has a constant probability of success. The binomial distribution has two parameters: n, the number of trials, and p, the probability of success in each trial. The probability of getting exactly k successes in n trials is given by the formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k) where (n choose k) is the binomial coefficient, which is equal to n! / (k! * (n-k)!) and represents the number of ways to choose k successes out of n trials. The mean or expected value of a binomial distribution is given by E(X) = n * p, and the variance is given by Var(X) = n * p * (1-p). The binomial distribution is widely used in statistics and probability theory, particularly in fields such as genetics, engineering, and finance, where it is used to model the probability of success or failure in a series of trials. Co...
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