What is Variance: Definition and 356 Discussions

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. In other words, it measures how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by




σ

2




{\displaystyle \sigma ^{2}}
,




s

2




{\displaystyle s^{2}}
, or



Var
⁡
(
X
)


{\displaystyle \operatorname {Var} (X)}
.

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  1. R

    Me the variance of the score function in exponential distribution

    please help me! the variance of the score function in exponential distribution Homework Statement My question is about exponential function, with its density function known as f(x;theta) = (1/theta) e^(-x/theta) for all x>0. where E(x) = theta, var(x) = theta^2 My question is, what...
  2. R

    Me the variance of the score function?

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  3. C

    Why is the variance of the Parzen density estimator infinite?

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  4. P

    Find mean and variance of X and Y

    Homework Statement I have found the marginal distribution for X and Y from a table. (No statistical regression, just simple table) How should I proceed in finding mean, variance an correlation coefficient of X and y? I am computing by hand. Thank you, Homework Equations The...
  5. T

    Prove the sample variance formula.

    Homework Statement Prove that the sample variance of a sample is given by S2 = \frac{\sum^{n}_{j=1}x_j^2 - \frac{1}{n} (\sum^{n}_{j=1}x_j)^2}{n-1} Homework Equations N/A The Attempt at a Solution For my purposes it is sufficient to show that: \sum^{n}_{j=1}(x_j -x_j^2) =...
  6. T

    Find the Variance of this distribution

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  7. D

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  8. G

    Bernoulli Variance: Calculating Var[Xi] as a Function of p

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  9. J

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  10. G

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  11. K

    What is the integral method for finding the mean in exponential distribution?

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  12. O

    Distribution arising from randomly distributed mean and variance

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  13. N

    Taylor expansion of gaussian integral with respect to variance

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  14. T

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  15. Matterwave

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  16. T

    Unbiased estimator of variance

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  17. D

    Expectation and Variance for Continous Uniform RV

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  18. C

    What is the correlation of X and Z in terms of variance and covariance?

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  19. K

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  20. D

    Statistical mechanics: energy variance of ensemble

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  21. D

    Statistical mechanics: energy variance of ensemble

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  22. G

    Variance of bootstrap sample of size n

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  23. G

    Estimating Population Variance from Observations

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  24. S

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  25. S

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  26. K

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  27. D

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  28. G

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  29. P

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  30. S

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  31. F

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  32. C

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  33. Y

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  34. G

    Work out the variance of the gamma

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  35. F

    What Is the Variance of an Eigenvector in a Hermitian Operator?

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  36. C

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  37. A

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  38. M

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  39. M

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  40. R

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  41. S

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  42. S

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  43. S

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  44. J

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  45. F

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  46. Cyrus

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  47. V

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  48. T

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  49. H

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  50. H

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