Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2004 / Paper 1 / 5 / b / i

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.