var(x) = E[(x - E(x))2]
= E[(x - E(x)) (x - E(x))] <-------------Expand into brackets
= E[x2 - xE(x) - xE(x) + (E(x))2] <---Simplify
= E[x2 - 2xE(x) + (E(x))2]
= E(x2) + E[-2xE(x)] + E[(E(x))2]
= E(x2) - 2E[xE(x)] + E[(E(x))2] <---Bring (-2) constant outside
= E(x2) - 2E(x)E[E(x)] + E[(E(x))2] <--- E[xE(x)] = E(x)E(x)
= E(x2) - 2E(x)E(x) + [E(x)]2 <----------E[E(x)] = E(x)
= E(x2) - 2[E(x)]2 + [E(x)]2
var(x) = E(x2) - [E(x)]2
The mathematician spent all day trying to derive the complex formula.
The answer depends on what information you have.
Total material variance is calculated by comparing the actual cost of materials used to the standard cost of materials that should have been used for the actual production level. The formula is: Total Material Variance = (Actual Quantity x Actual Price) - (Standard Quantity x Standard Price). This variance can be further broken down into material price variance and material quantity variance for more detailed analysis.
Area = 0.5*(sum of parallel sides)*height
Variance is a characteristic parameter of a probability distribution: it is not a statistic. In any particular situation (with a few strange exceptions) it has only one value and therefore cannot have any bias.
var(X) = (xm/a - 1)2 a/a-2 . If a < or equal to 2, the variance does not exist.
b-a/6
Ozone layer has no formula. However there is a formula for ozone and that is O3.
The mathematician spent all day trying to derive the complex formula.
The answer depends on what information you have.
To calculate portfolio variance in Excel, you can use the formula SUMPRODUCT(COVARIANCE.S(array1,array2),array1,array2), where array1 and array2 are the returns of the individual assets in your portfolio. This formula takes into account the covariance between the assets and their individual variances to calculate the overall portfolio variance.
You calculate it using the appropriate formula, which, given the limitations of this site, is not easy to reproduce. However, you can easily Google the formula.
Classic IB student...
Total material variance is calculated by comparing the actual cost of materials used to the standard cost of materials that should have been used for the actual production level. The formula is: Total Material Variance = (Actual Quantity x Actual Price) - (Standard Quantity x Standard Price). This variance can be further broken down into material price variance and material quantity variance for more detailed analysis.
The total deviation formula used to calculate the overall variance in a dataset is the sum of the squared differences between each data point and the mean of the dataset, divided by the total number of data points.
the Taylor series of sinx
Area = 0.5*(sum of parallel sides)*height