Problem 2. Continuous Random Variables
2 points possible (graded, results hidden)
Let π and π be independent continuous random variables that are uniformly distributed on (0,1) . Let π»=(π+2)π . Find the probability π(lnπ»β₯π§) where π§ is a given number that satisfies ππ§<2 . Your answer should be a function of π§ .
Hint: Condition on π .
1. P(ln H > z) = unanswered
2. Let π be a standard normal random variable, and let πΉπ(π₯) be its CDF. Consider the random variable π=πΉπ(π) . Find the PDF ππ(π§) of π . Note that ππ(π§) takes values in (0,1) .
fz(z) = unanswered
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