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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

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, assume the following

X~N(46,3) (ie E(X) = 46 and Var(X) = 3)

Y~N(92,8)

Cov(X,Y) = 0.5

What is the variance in the amount of liquid that ends up in the cup, ie Var(X+Y)?

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