We choose independently two numbers at random from the inter

We choose independently two numbers at random from the interval [0, 1] with uniform pdf. What is the pdf of their sum?

Solution

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )

f(x) = 1/(b-a) = 1 / (1-0) = 1 / 1 = 1

Mean = a + b / 2 = 0.5
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 0.289