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# Independent random variable question urgent thank you!

Tue 23 Apr, 2013 05:29 am
Suppose X and Y are independent random variables with μ_x=3, σ_x^2=2, μ_y=4, σ_y^2=5 and that W=5X+2Y.

What is the mean of W?
What is the variance of W?
What is the standard deviation of W?

Very urgent!! and working/formulae would be brilliant! thanks in advance
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engineer

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Tue 23 Apr, 2013 06:53 am
@taniae00,
The mean of W = 5μ_x + 2μ_y = 15 + 8 = 23
A formula for the variance of W can be found here under the "basic properties" heading. If the two functions x and y are unrelated, then the formula is variance of (aX + bY) = a^2 variance X + b^2 variance Y.
The standard deviation of W is the square root of the variance.
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