Probability Help: Formulas for Random Variables with Mean 5 and Variance 12

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To solve for the expected value of y, use the formula E(y) = E(3 + 9x) = 3 + 9E(x), which results in an expected value of 3 + 9*5 = 48. For the variance of y, apply Var(y) = Var(9x) = 9^2 * Var(x), leading to a variance of 81*12 = 972, and the standard deviation is the square root of the variance. Regarding the distribution of y, since x is normally distributed, y will also be normally distributed due to linear transformation properties. Understanding these formulas will help in addressing the questions about random variables effectively.
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So I took probability last year, and for one of my classes we have an optional refresher worksheet, but I cannot remember how to deal with random variables :(

I don't need the answer -- just some guidance on what formulas to use please!

x is a random variable with mean 5 and variance 12.

y = 3 + 9x

a) what is the expected valued of y?

b) what is the variance and SD of y?

c) is y normally distributed?

thank you so much!
 
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Welcome to PF, xhallie! :smile:

Here's a page I just googled, which I believe answers your questions:
http://www.kaspercpa.com/statisticalreview.htm
 

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