# Exam P Practice Problem 18 – Variance of a Sum

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Problem 18A
A company is at risk for two financial losses $X$ and $Y$. The company is at risk for no other financial risk. Suppose that $X$ and $Y$ are jointly distributed according to the density function $f(x,y)=4 \ x^2$ where $0 and $0. What is the variance of the total financial loss faced by this company?

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Problem 18B
A company is at risk for two financial losses $X$ and $Y$. The company is at risk for no other financial risk. Suppose that $X$ and $Y$ are jointly distributed according to the density function $f(x,y)=\alpha^2 \ e^{-\alpha \ x}$ where $\alpha>0$ and $x>0$ and $0. What is the variance of the total financial loss faced by this company?

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