Examples of using Random variables in English and their translations into Romanian
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Random variables?
The variance of a sum of two random variables is given by.
Random Variables, 518.
For a sequence X1,…,Xn of random variables, and constants a1,…, an, we have.
Random variables whose covariance is zero are called uncorrelated.
Three probability density functions(PDF) of random variables with log-normal distributions.
If the random variables X 1,…, X N{\displaystyle X_{1},\dots,X_{N}} are such that.
Here Cov(⋅,⋅) is the covariance,which is zero for independent random variables(if it exists).
Random variables and discrete laws of probability(binomial, hypergeometric, Poisson, Pascal, geometric).
Stochastic programming studies the case in which some of the constraints or parameters depend on random variables.
In general we have for the sum of N{\displaystyle N} random variables{ X 1,…, X N}{\displaystyle\{X_{1},\dots,X_{N}\}}.
Since the Yi are selected randomly, both Y¯{\displaystyle{\overline{Y}}} and σ Y 2{\displaystyle\sigma_{Y}^{2}}are random variables.
A useful identity to compute the covariance between two random variables X, Y{\displaystyle X, Y} is the Hoeffding's Covariance Identity:[7].
Regression analysis is a statistical method for investigating the dependence of random variables on variables. .
Being a function of random variables, the sample variance is itself a random variable, and it is natural to study its distribution.
The log-likelihood is easier to maximize,especially for the multiplied likelihoods for independent random variables.[73].
The components are regarded as random variables, and may be grouped into two categories according to the method used to estimate their numerical values.
Differential Entropy: Extending discrete entropy to the continuous case- The Shannon entropy is restricted to random variables taking discrete values.
Applications==The concept of the probability distribution and the random variables which they describe underlies the mathematical discipline of probability theory, and the science of statistics.
The general formula for variance decomposition or the law of total variance is: If X{\displaystyle X} and Y{\displaystyle Y}are two random variables, and the variance of X{\displaystyle X} exists.
The covariance between two jointly distributed real-valued random variables X and Y with finite second moments is defined as the expected product of their deviations from their individual expected values:[3].
Topics include-- probability, binomial and normal distributions,2 sample hypothesis tests for means and proportions, applied combinative… something, discrete and continuous random variables.
Therefore, c T X{\displaystyle c^{T}X}is a linear combination of these random variables, where c T{\displaystyle c^{T}} denotes the transpose of c{\displaystyle c}.
The sample mean and the sample covariance matrix are unbiased estimates of the mean and the covariance matrix of the random vector X{\displaystyle\textstyle\mathbf{X}}, a vector whose jth element(j= 1,…, K)is one of the random variables.
If X, Y, W, andV are real-valued random variables and a, b, c, d are constant("constant" in this context means non-random), then the following facts are a consequence of the definition of covariance.
In fact these properties imply that the covariance defines an inner product over the quotient vector space obtained by taking the subspace of random variables with finite second moment and identifying any two that differ by a constant.
Instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.
When the logarithm of a random variable has a normal distribution, the variable is said to have a log-normal distribution.[71] Log-normal distributions are encountered in many fields, wherever a variable is formed as the product of many independent positive random variables, for example in the study of turbulence.[72].
It follows immediately from the expression given earlier that if the random variables X 1,…, X N{\displaystyle X_{1},\dots,X_{N}} are uncorrelated, then the variance of their sum is equal to the sum of their variances, or.
Bilinear: for constants a and b and random variables X, Y, Z, cov(aX+ bY, Z)= a cov(X, Z)+ b cov(Y, Z); symmetric: cov(X, Y)= cov(Y, X); positive semi-definite: σ2(X)= cov(X, X)≥ 0 for all random variables X, and cov(X, X)= 0 implies that X is a constant random variable(K).