Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: X+Y

opatovaL 2021-06-01 Answered

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: \(X+Y\)

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Expert Answer

timbalemX
Answered 2021-06-02 Author has 10640 answers

The mean and standard deviation is as follows:
\(E(X+Y)=E(X)+E(Y)\)
\(=80+12\)
\(=92\)
\(V(X+Y)=V(X)+V(Y)\)
\(SD(X+Y)=\sqrt{V(X)+V(Y)}\)
\(=\sqrt{12^{2}+3^{2}}\)
\(=\sqrt{153}\)
\(=12.3693\)

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