How to use the variance of a sum of two variables calculator
Find the variance and standard deviation of the sum of two random variables, including their covariance. Enter variance of x, variance of y, covariance of x and y in the fields above; the variance of x + y, standard deviation of x + y are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “variance of sum”, “covariance sum variance”, “standard deviation of sum”, “calculate variance of a sum of two variables”, “find variance of x + y”.
Formula
Variables
- v1 — Variance of X
- v2 — Variance of Y
- cov — Covariance of X and Y
Worked example
With variance of x = 4, variance of y = 9, covariance of x and y = 0.5, the calculator gives variance of x + y ≈ 14; standard deviation of x + y ≈ 3.741657.
Frequently asked questions
What is the variance of a sum of two variables calculator used for?
Find the variance and standard deviation of the sum of two random variables, including their covariance. It helps with questions such as “variance of sum”, “covariance sum variance”, “standard deviation of sum”.
What is the formula for the variance of a sum of two variables calculation?
Variance of X + Y = v1+v2+2 × cov. Standard deviation of X + Y = √([Variance of X + Y]). Here v1 is variance of x, v2 is variance of y, cov is covariance of x and y.
What inputs do I need for the variance of a sum of two variables calculator?
You need variance of x, variance of y, covariance of x and y. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the variance of a sum of two variables calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the variance of a sum of two variables result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.