Question

The sum of two independent uniformly distributed random variables over [0,1] is another uniformly distributed random variable over [0,1].

A. True
B. False

Answer 1

B. False

Explanation:

the sum will be within [0,2].

Take for example the independent random values 0.8 and 0.7.

They add up to 1.5, which is outside [0,1]. That's why the statement cannot be true.