Variance of Sum of Independent Random Variables Calculator

✖Variance of Random Variable X is the measure of variability or dispersion of random variable X.ⓘ Variance of Random Variable X [σ²Random X]			+10% -10%
✖Variance of Random Variable Y is the measure of variability or dispersion of random variable Y.ⓘ Variance of Random Variable Y [σ²Random Y]			+10% -10%

✖Variance of Sum of Independent Random Variables is the variance calculated when two or more independent random variables are added together.ⓘ Variance of Sum of Independent Random Variables [σ²Sum]

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Formula

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Variance of Sum of Independent Random Variables

Formula

`("σ"^{"2"}"Sum") = ("σ"^{"2"}"Random X")+("σ"^{"2"}"Random Y")`

Example

`"25"="9"+"16"`

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Variance of Sum of Independent Random Variables Solution

STEP 0: Pre-Calculation Summary

Formula Used

Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y
σ²Sum = σ²Random X+σ²Random Y
This formula uses 3 Variables

Variables Used

Variance of Sum of Independent Random Variables - Variance of Sum of Independent Random Variables is the variance calculated when two or more independent random variables are added together.
Variance of Random Variable X - Variance of Random Variable X is the measure of variability or dispersion of random variable X.
Variance of Random Variable Y - Variance of Random Variable Y is the measure of variability or dispersion of random variable Y.

STEP 1: Convert Input(s) to Base Unit

Variance of Random Variable X: 9 --> No Conversion Required
Variance of Random Variable Y: 16 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ²Sum = σ²Random X+σ²Random Y --> 9+16

Evaluating ... ...

σ²Sum = 25

STEP 3: Convert Result to Output's Unit

25 --> No Conversion Required

FINAL ANSWER

25 <-- Variance of Sum of Independent Random Variables

(Calculation completed in 00.004 seconds)

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Variance of Sum of Independent Random Variables

Go Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y

Variance of Scalar Multiple of Random Variable

Go Variance of Scalar Multiple of Random Variable = (Scalar Value c^2)*Variance of Random Variable X

Variance given Standard Deviation

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Variance of Sum of Independent Random Variables Formula

Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y
σ²Sum = σ²Random X+σ²Random Y

What is Variance and the importance of Variance in Statistics?

Variance is a statistical tool used to analyze a statistical data. The word Variance is actually derived from the word variety that in terms of statistics means the difference among various scores and readings. Basically it is the expectation of the squared deviation of the associated random variable from its population mean or sample mean. Variance ensures accuracy as more Variance is considered good as compared to the low Variance or absolutely absence of any Variance. Variance in statistics is important as in a measurement it allows us to measure the dispersion of the set of the variables around their mean. These set of the variables are the variables that are being measured or analyzed. The presence of the Variance allows a statistician to draw some meaningful conclusion from the data. The advantage of Variance is that it treats all deviations from the mean as the same regardless of their direction.

How to Calculate Variance of Sum of Independent Random Variables?

Variance of Sum of Independent Random Variables calculator uses Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y to calculate the Variance of Sum of Independent Random Variables, Variance of Sum of Independent Random Variables formula is defined as the variance calculated when two or more independent random variables are added together. Variance of Sum of Independent Random Variables is denoted by σ²Sum symbol.

How to calculate Variance of Sum of Independent Random Variables using this online calculator? To use this online calculator for Variance of Sum of Independent Random Variables, enter Variance of Random Variable X (σ²Random X) & Variance of Random Variable Y (σ²Random Y) and hit the calculate button. Here is how the Variance of Sum of Independent Random Variables calculation can be explained with given input values -> 25 = 9+16.

FAQ

What is Variance of Sum of Independent Random Variables?

Variance of Sum of Independent Random Variables formula is defined as the variance calculated when two or more independent random variables are added together and is represented as σ²Sum = σ²Random X+σ²Random Y or Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y. Variance of Random Variable X is the measure of variability or dispersion of random variable X & Variance of Random Variable Y is the measure of variability or dispersion of random variable Y.

How to calculate Variance of Sum of Independent Random Variables?

Variance of Sum of Independent Random Variables formula is defined as the variance calculated when two or more independent random variables are added together is calculated using Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y. To calculate Variance of Sum of Independent Random Variables, you need Variance of Random Variable X (σ²Random X) & Variance of Random Variable Y (σ²Random Y). With our tool, you need to enter the respective value for Variance of Random Variable X & Variance of Random Variable Y and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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