1. Let X ~ U[0; 1]. Find the PDF of each of the following:
(a) X^3 - 3X;
(b) (X - 1/2)^2
2. Let X ~ U[0; 1]. Find the PDF of ln ln 1/X .
Here,
X ~ Uniform(0, 1)
The probability density function of X is
The cumulative distribution function of X is
= 1, x >= 1
The cumulative distribution function of Y = ln 1 / X is
The probability density function of Y is
So, Y ~ Exponential(1)
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