Let X 1 and X 2 be independent random variables having the uniform density with = 0 and = 1. Referring to Figure

Let X₁ and X₂ be independent random variables having the uniform density with α = 0 and β = 1. Referring to Figure 7.2, find expressions for the distribution function of Y = X1 + X2 for 

(a) y ≤ 0; 

(b) 0

(c) 1

(d) y ≥ 2. Also find the probability density of Y. 

Figure 7.2

1