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706
Probability and Random Variables
Appendix B
or
ƒ ƒ
ƒ ƒ ƒ ƒ
1>2p
+
1>2p
, y … A
f y (y) = µ
2A 2 - y 2 - 2A 2 - y 2
0, y elsewhere
0, y 6 -A
ƒ ƒ 1
f y (y) = e
p2A 2 - y 2, y … A
0, y 7 A
(B–71)
which is the PDF for a sinusoid as given first by Eq. (B–67). This result is intuitively obvious,
since we realize that a sinusoidal waveform spends most of its time near its peak values and
passes through zero relatively rapidly. Thus, the PDF should peak up at +A and -A V. See
Example B–09.m for a plot of Eq. (B–71).
Example B–10 PDF FOR THE OUTPUT OF A DIODE CHARACTERISTIC
Assume that a diode current-voltage characteristic is modeled by the ideal characteristic shown in
Fig. B–10, where y is the current through the diode and x is the voltage across the diode. This type
of characteristic is also called half-wave linear rectification.
y = e Bx, x 7 0
0, x … 0
(B–72)
y=h(x)
y
Slope=B
x
f y (y)
f x (x)
x
Figure B–10
Evaluation of the PDF out of a diode characteristic for Ex. B–10.