[Math] How to calculate new standard deviation based on formula given only the mean and set standard deviations

meansstandard deviationstatistics

I currently have the mean and standard deviation, I need to calculate the new standard deviation given a formula:

µX = 9.5 and µY = 6.8
σX = 0.4 and σY = 0.1

with the equation X-Y

What steps do I go though to calculate the new mean and standard deviation?

Thanks in advance!

Best Answer

Variance($V$) of $(X-Y)=V(X)+V(Y)-2Cov(X,Y)$ where $Cov(X,Y)$ is the covariance between $X$ and $Y$.

Mean($\mu$) of $(X-Y)=\mu(X)-\mu(Y)$

So you need information regarding the covariance to calculate the answers properly if $X$ and $Y$ are not independent.

EDIT: $$Cov(X,Y)=\sum_{i=1}^{n}\frac{(x_i-\bar x)(y_i-\bar y)}{\sigma_x\sigma_y}$$

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