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April 27th, 2017, 10:33 AM   #1
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Finding a cdf

A number U is chosen at random in the interval [0, 1].

(b) S = U(1 − U) < 1/4.

13 Find the cumulative distribution function F and the density function f for
the random variables S.
Attempt: I tried to use the theorem P (Y is less than or equal to y). Then I got P(U (1-U) is less than or equal to y) then I got P (u-u^2 is less than or equal to y). Then, I factoed out a u to get
P(u is less than to equal to y/(1-u)). I tried to isolate E the U, but there was no way I could getthe cdf that way. How should I find the cdf for this problem?
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