(1) Find the density function of U₁ + U₂, where U₁ and U₂ are independent, and U₁ has a Uniform(0,2) distribution but U₂ has a Uniform(0,3) distribution.

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Let X and Y be two independent uniformly distributed random variables over the intervals (0, 1) and (0, 2), respectively. Find the probability density function of X/Y

Let f (x, y) be the joint probability density function of X and Y, G be the probability distri- bution function of X/ Y, and g be the probability density function of X/ Y. We have that f (x, y ) = 1/2 0 1/2, P ( # 21 ) = 1" ( 1, zay ) ax = 1- 2. (Draw appropriate figures to verify the limits of these integrals.) Therefore, 0 1