Covariance Question:

yayayaygeralt

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Apr 11, 2022
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Hi all, I have this covariance question that I am stuck on and have no idea how to solve; any input would be so much appreciated!

A coffee vending machine adds brewed coffee and then hot water to make a cup of coffee. Let X = the amount of coffee added and Y = amount of water added, assuming the following:

X~N(45,3) (ie E(X) = 45 and Var(X) = 3)
Y~N(95,9)
Cov(X,Y) = 1.8

What is the expected amount of liquid that ends up in the cup, ie E(X+Y)
 
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