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Let U,V be i.i.d. random variables uniformly distributed in [0,1]. Compute the following quantities: E[|U−V|]= P(U=V)=...

Let U,V be i.i.d. random variables uniformly distributed in [0,1]. Compute the following quantities:

E[|U−V|]=

P(U=V)=

P(U≤V)=

Math   Statistics-And-Probability   
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Answer #1

Given are IID uniform random variables with .

First we find the distribution of . Let . Then using CDF method,

The PDF is

Since are IID random variables because of symmetry, . See figure below.

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