Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 0.5Y

foass77W 2021-05-27 Answered
Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 0.5Y

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Nichole Watt
Answered 2021-05-28 Author has 19372 answers
The mean and standard deviation is as follows:
E(0.5Y)=0.5E(Y)
\(=0.5\times 12\)
=6
\(V(0.5Y)=0.5^{2}V(Y)\)
\(=0.5^{2}V(Y)\)
\(SD(0.5Y)=0.5\times SD(Y)\)
\(=0.5\times 3\)
=1.5
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