Problem 4. Suppose X and Y are independent random variables with the following densi- ties: _ e&quot;z lfI'ZO _ ye&quot;?
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Problem 4. Suppose X and Y are independent random variables with the following densi- ties: _ e&quot;z lfI'ZO _ ye&quot;? inyO f&quot;(\$)_{0 if33&lt;0 My)_{0 ify&lt;0 You may recognize that X has the density of an exponential random variable with parameter A = 1, and Y has the density of the sum of two independent exponential random variables each with parameter A = 1. Compute the density of the random variable Z = X + Y.

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