ECE 547 Project #1 – Fall 2008
1a)
1b)
P(U > x) for values of x
(0.5,1) can be plotted as the following:
Figure 1 P(U>x)
In order to calculate
P (U>x)
, the interval [0, 1] is divided into intervals of width 0.01. For each value of
x
i
the corresponding frequency
f
i
out of a total of
N=
10
5
numbers such that
U> x
i
was calculated. Then
using
P (U> x
i
)
=
f
i
/
N,
the probabilities were calculated at each of the
x
i
..
The pairs of points (
x
i
,
P (U> x
i
)
)
were plotted
Note that P(U>x) = 1
‐
x. The plot is as expected.
2a)
Generation of Exponentially Distributed Random Numbers
The cumulative distribution function of the exponentially distributed random variable is
0
( )
( )
x
X
X
F
x
f
x dx
=
∫
where
( )
x
X
f
x
e
λ
λ
−
=
is the pdf of the exponentially distributed random variable
with parameter
λ
.
Choose a function
G ( )
such that

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