Uniform density and integral
Let X_1 and X_2 be independent random variables having the uniform density with a = 0 (alpha = 0) and b = 1 (beta = 1). Find expression for the distribution function of Y = X_1 + X_2 for 1 <y < 2. According to the book, the final answer is 1 - 1/2(2 - y)^2, but I cannot construct the integral expression, from which I would get this final result. Please help me construct this integral. Can you please show me how to calculate the area of appropriate region of the unit square?