The following voltage waveform is to be sampled at a random time τ over a period of .
a)What is the probability of that the sampled value v(t) <-0,5
b)What is the probability of that the sampled value v(t)>1.25
c)What is the probability of that the sampled value v(t)=1,25
d)What is the probability of that the sampled value v(t)= -0,5

2.

3. c) 0.1, d) 0.3. I'll leave the others for you.

4. d) must be 0

5. In practice, the probabilities depend on the accuracy of the measurement of v during the sampling process. If you don't take this into account, I wouldn't be surprised if you could construct some anomalies, since the probability of finding any one point on a sloping straight line will be 0, and the probability of finding a position somewhere along the line will be greater than zero.

6. yes it is true. But I wonder while solving this problem is, what process do we use?

7. Originally Posted by mecnun9
yes it is true. But I wonder while solving this problem is, what process do we use?
The conceptually simplest way is to get the probability of getting a value between v- $\epsilon$/2 and v + $\epsilon$/2, and at the end of your calculation take the limit as $\epsilon$ goes to zero. Then to cover a region with measurements at a "point at a time," the points will be a distance $\epsilon$ apart. With care, you will get no anomalies. In real life, you could take $\epsilon$ to be the measurement error in your instrument and sum rather than integrate.

8. Originally Posted by mecnun9
d) must be 0
You're right - I misread the picture. Somehow I saw it constant for an interval.

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