Binomial distribution and Random variable

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Difference between Binomial distribution and Random variable

Binomial distribution vs. Random variable

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 sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q. In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

Boolean-valued function

A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f: X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B.

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Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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Fair coin

In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin.

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Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

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Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Outcome (probability)

In probability theory, an outcome is a possible result of an experiment.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Probability mass function

In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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Random number generation

Random number generation is the generation of a sequence of numbers or symbols that cannot be reasonably predicted better than by a random chance, usually through a hardware random-number generator (RNG).

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Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

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