X and Y are independent random variables. X is normally distributed with mean 1 and variance 1. Y is normally distributed with mean 3 and variance 5. What is the variance of Y - 2X?

Question

Sam Dunlap

Mathematics

23 October, 20:25

X and Y are independent random variables. X is normally distributed with mean 1 and variance 1. Y is normally distributed with mean 3 and variance 5. What is the variance of Y - 2X?

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Step-by-step explanation:

Equation of variance:

Total Variance = sum (i=1, N) {c^2, variance^2}

= c1^2*variance1^2 + c2^2*variance2^2 + ...

Variance of X = 1

Variance of Y = 5

Variance of Y - 2X = (1^2) * (5) - (2^2) * * (1)

= 5 - 4 = 1