Introduction to Probability Function (Part 1)

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

  1. Binomial Distribution

—In a binomial distribution a trial can have only two possible outcomes (success or failure)

—A fixed number of trials (n) is performed, with each trial independent of the prior

—Because the n trials are independent, the outcome of one trial cannot help predict the outcome of another trial

—The probability of a success and probability of a failure remain the same between trials

—The random variable X = the number of successes obtained in the n independent trials.

—If p is the probability of a success on one trial, and q is the probability of a failure on one trial

—The mean = n*p

—The variance = n*p*q

A function that generates binomial probabilities is given below. It represents the probability of exactly x successes in n trials in a binomial experiment.

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