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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 which says that the equation ? 2 − ?1? + ?2 = 0 has no real roots. Find the conditional c.d.f. of ? when ? is true

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orchestra answered 2 years ago
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