Suppose that U has a uniform distribution on [0, 1] and that, conditional on U = u, the distribution of V is uniform on [0, u]. What is the probability density function of V?
1 Answer
Probability density of random variable
Explanation:
The probability density
(a) random variable
(b) random variable
These two above factors are two independent random variable, so the probabilities of combined events must be multiplied.
Now the probability density of
Just to check, integral of this probability density from
Graphically, the probability density of random variable
graph{-ln(x) [-.1, 1, -5, 5]}
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