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Let 1 and 2 be two independent random variables with uniform distribution on [0, 1]. 1. Write down the joint cumulative distribution function and joint probability density function of 1 + 2 and 12. 2. Write down the covariance between 1 + 2 and 12. 3. Let be the largest magnitude (absolute value) of a root of the equation 2 1 + 2 = 0. Let be the random event that says that the equation 2 1 +2 = 0 has no real roots.

Find the conditional c.d.f. of when is false,