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Use the unit step function to write a single expression for the cumulative distribution function for the mixed random variable Y of Example 2.3, having
| F_{Y}(u)=0 | For u \lt 0 |
| F_{Y}(u)=0.05(u+4) | For 0 \leq u \lt 10 |
| F_{X}(u)=1 | For u \geq 10 |
The discontinuous F_{Y}(u) is exactly given by
F_{Y}(u)=0.05(u+4)[U(u-4)-U(u-10)]Or
F_{Y}(u)=0.05(u+4)U(u)+(0.8-0.05u)U(u-10)