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    Uniform Distributions

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    1) Suppose that A, B, C are independent random variables, each being uniformly distributed over (0,1). What is the joint cumulative distribution function of A, B, C? What is the probability that all of the roots of the equation Ax^2+Bx+C=0 are real?

    2) If X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter 1, find the distribution of (a) Z=X+Y and (b) Z=X/Y. Assume independence.

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