Solution
= Solution
The continuous nonnegative part has total mass $\lim_{y\to\infty}(1-e^{-y})/2=1/2$. The remaining mass is at $-1$, giving $\boxed{m=1/2}$. This is a <mixed probability distribution>, specifically a <mixture of a point mass and an exponential distribution>; its atom must be included in normalization.