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Sagot :
Any value x not explicitly associated with a positive probability is taken as P(X=x) = 0. The function pX(x)= P(X=x) for any x in the range of X is given as a probability. It is often called the probability mass function of a discrete random variable X.
Binomial Distribution:
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own It has a Boolean result: success (for probability p) or failure (for probability q = 1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.
The binomial distribution is commonly used to model the number of successes in a sample of size n drawn from a population of size N with replacement. If sampling is performed without replacement, the resulting distribution is hypergeometric rather than binomial because the plots are not independent. However, for N much larger than n, the binomial distribution remains a good approximation and is widely used.
In the binomial distribution, the trials to be investigated must have the same probability of success. For example, if you toss a coin, the probability of flipping the coin is 1/2. 0.5 for each trial because there are only two possibilities.
Binomial Random Variable:
This is a special kind of discrete random variable. A binomial random variable counts the number of times a particular event occurs over a fixed number of trials or trials.
Learn more about Random Variable:
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