Problem 3 Probabilit y spaces a A probability experiment con

Problem 3 Probabilit y spaces (a) A probability experiment consists of measuring a voltage value, say V, in the range -10 to +10 volts inclusive. What is the sample space, S, for the experiment? (b) Suppose that the random voltage in part (a) is input to a half-wave rectifier before we take the measure- ment. The rectifier simply takes the absolute value of the variable V: V Rectifier X VI. (1) If the probability experiment consists of measuring a value of X (rather than V), what is the sample space, say SX (c) Which sample space above, S, or Sx, contains more points (d) Repeat parts (a) and (b) if -3 volts is added to the variable V ore any measurements are taken

Solution

(a) The sample space for this experiment is all values contained in the range (-10, +10) volts.

(b) The sample space of X when X=|V| is all values contained in the range (0, 10) volts because the negative volts is turn to be positive.

(c) The sample space S contained more points regardings to S_X because the S space contained the positive as weel as the negative points in the sample space.

(d) When we add -3 volts is added , the sample space of S is (-13, 7) volts where the sample space of S_X is (7, 13)