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

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
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