# Getting the variance of a data set when only given the mean and variance of a related data set.

Call x the atmospheric carbon dioxide level in parts per million by volume. Call y the change in the earth’s surface temperature over the next 50 years, in degrees celsius. Suppose that climate scientists estimate this relationship:

y = 0.20 · (x − 390).

Suppose x has a mean of 410 and a variance of 18. Find the mean and variance of the change in the temperature.

I have already solved for the mean of the temperature, it came out to be 4 but from there I am unsure of how to go about taking the data given and finding the variance of the temperature.

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## 1 Answer

y=(-78)+.2x

now if x has a mean 410, then y will have a mean = (-78)+.2 X 410 = 4 and variance = .2 ^ 2 X 18 = 0.72

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How come you squared the .2 and dropped the 390 when solving for variance? – Alex Oct 14 '12 at 21:34
Given a random variable X has a mean u and variance v, then another random variable y=a1+a2.X (a2 > 0) , random variable y will have a mean = a1+a2.u and a variance = a2 ^ 2 . v , there's a long proof of this for which I think I need to consult some book – Diptarag Oct 14 '12 at 21:41