Question: 13. Let X 1 , X 2 and X 3 be independent continuous random variable's each uniformly distributed in the interval [0,20]. Think of these

13. Let X₁, X₂ and X₃ be independent continuous random variable's each uniformly distributed in the interval [0,20]. Think of these as arrival times of 3 people at a bus stop between 8:40 and 9:00.Let Y denote the middle of the three values. Y is always the second smallest of X₁, X₂ and X₃, so Y = X₍₂₎.

Find the joint density of X₍₁₎, X₍₂₎, and X_{(3) .}
Find the density of Y by integrating X₍₁₎ and X₍₃₎ out.

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