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1. (5 points) Let X be an Exponential(10) random variable, which is inde- pendent of Y, an Exponential(5) random variable. Find the density fz(z) of

1. (5 points) Let X be an Exponential(10) random variable, which is inde- pendent of Y, an Exponential(5) random variable. Find the density fz(z) of the random variable Z = max{ X, Y}. Hint: Find the CDF of Z first

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