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To find the marginal distribution of uniform random variable

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I cannot prove the solution given for the following Conditional Joint Uniform Distribution. I have a fairly detailed answer provided by my professor, but I cannot do the Integration to prove.

Could you please provide a detailed step by step integration to backup the given answer. I am sure I am missing a basic either Uniform observation OR just not setting up the Uniform Integrals properly.

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Solution Summary

Two uniform distribution is considered under some specific condition where the marginal is derived.