Let the random variable X represent the DC voltage output from some force transducer, and let the distribution be uniform on the set [-4,16] such that F_{X}(u)=0.05 (u+4) for -4 \leq u \leq 16. Of course, F_{X}(u) is zero to the left and unity to the right of the [-4,16] interval. Now let another (mixed) random variable Y represent the output from a voltmeter that reads only from zero to 10 volts and that has X as the input. Whenever 0 \leq X \leq 10 we will have Y = X, but we will get Y=0 whenever X \lt 0, and Y=10 whenever X \gt 10. Find the cumulative distribution function for Y.
Chapter 2
Q. 2.3
Step-by-Step
Verified Solution
From P(Y \leq u) we get
| 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 |
This F_{Y}(u) function for this mixed random variable has discontinuities of 0.2 at u=0 and 0.3 at u=10, representing the finite probabilities that Y takes on these two particular values.