# 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

#### 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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