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In: Statistics and Probability

Let ?1 and ?2 be two independent random variables with uniform distribution on [0, 1]. 1....

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 ?1?2.
2. Write down the covariance between ?1 + ?2 and ?1?2.
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,

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orchestra answered 2 years ago
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