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Variance of discrete random variable.
Varx y formula. Varx e x m 2 where m is the expected value ex this can also be written as. Varxy varx vary standard deviation. The formula for variance for a sample set of data is.
The standard deviation of x is the square root of varx. Variance s2 dfracsigma xi overlinex2n 1 variance formula. When x and y are independent random variables.
Pros and cons of value at risk var there are a few pros and some significant cons to using var in risk measurement. Varx ex 2 m 2. Varxy varx vary 2covxy.
Note that the covariance of a random variable with itself is just the variance of that random variable. While variance is usually easier to work with when doing computations it is somewhat difficult to interpret because it is expressed in squared units. The formula for variance of a is the sum of the squared differences between each data point and the mean divided by the number of data values.
Note that the variance does not behave in the same way as expectation when we multiply and add constants to random variables. See derivation from anonymous commenter i cant get math in html for my blog so god bless him. In probability theory and statistics variance is the expectation of the squared deviation of a random variable from its meaninformally it measures how far a set of numbers is spread out from their average value.
For continuous random variable with mean value m and probability density function fx. 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. On the plus side the measurement is widely used by financial industry.
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