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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
What else can I help you with?
What is a sentence using the word derive?
The mathematician spent all day trying to derive the complex formula.
How do you derive work done formula?
The answer depends on what information you have.
How do you calculate total material variance?
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.
How can you derive a formula for the area of a trapezoid?
Area = 0.5*(sum of parallel sides)*height
When do we use the unbiased formula of variance?
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.
How do you derive variance of Pareto distribution?
var(X) = (xm/a - 1)2 a/a-2 . If a < or equal to 2, the variance does not exist.
What is the formula for calculating variance and standard deviation?
b-a/6
How do you derive the formula of ozone layer?
Ozone layer has no formula. However there is a formula for ozone and that is O3.
What is a sentence using the word derive?
The mathematician spent all day trying to derive the complex formula.
How do you derive work done formula?
The answer depends on what information you have.
How can I calculate portfolio variance in Excel?
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.
How do you find 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.
How do you derive formula for finding the denominator of lapsac fraction?
Classic IB student...
How do you calculate total material variance?
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.
What is the total deviation formula used to calculate the overall variance in a dataset?
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.
Derive recursion formula for sin by using Taylor's Series?
the Taylor series of sinx
How can you derive a formula for the area of a trapezoid?
Area = 0.5*(sum of parallel sides)*height
