Biomedical Engineering Reference
In-Depth Information
z (x)
=
1
x
−
2
−
1
1
2
3
−
1
FIGURE 6.12:
Plot for Problem 15.
15. Random variable
x
has the CDF
⎧
⎨
0
,
α <
−
1
F
x
(
α
)
=
0
.
25(
α
+
1)
,
−
1
≤
α<
3
⎩
1
,
3
≤
α.
Find the CDF
F
z
, with RV
z
g
(
x
), and
g
(
x
) shown in Figure 6.12. Assume that
g
(
x
) is a second degree polynomial for
x
=
0.
16. The voltage
x
in Figure 6.13 is a random variable which is uniformly distributed from
−
≥
1 to 2. Find the PDF
f
z
. Assume the diode is ideal.
17. The voltage
x
in Figure 6.14 is a Gaussian random variable with mean
η
x
=
0 and
3. Find the PDF
f
z
. Assume the diodes are ideal.
18. The voltage
x
in Figure 6.15 is a Gaussian random variable with mean
standard deviation
σ
x
=
η
=
1 and
x
standard deviation
σ
=
1. Find the PDF
f
z
. Assume the diode and the operational
x
amplifier are ideal.
19. Random variable
x
is Gaussian with mean
η
=
0 and standard deviation
σ
=
1. With
x
x
z
=
g
(
x
) shown in Figure 6.16, find the PDF
f
z
.
+
+
1
K
Ω
x
3
K
Ω
z
−
−
FIGURE 6.13:
Circuit for Problem 16.
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