ELEC210 Spring 2011 Homework4
1.
The random variable X has cdf as shown in the figure below:
(a)
What type of random variable is X?
(b)
Find the following probabilities:
,
,
,
,
,
.
2.
A point is selected at random inside a square defined by
.
Assume the point is equally likely to fall anywhere in the square. Let the random variable
Z be given by the minimum of the two coordinates of the point.
(a)
Find the sample space S of the coordinates of the point and the sample space of Z,
.
(b)
Show the mapping from S to
.
(c)
Find the region in the square corresponding to the event
.
(d)
Find the cdf of Z.
(e)
Use the cdf to find:
.
3.
A random variable X has pdf:
(a)
Find c.
(b)
Find
.
(c)
Find
.
(d)
Find the mean and variance of X.
4.
A limiter is shown in figure below:
(a)
Find an expression for the mean and variance of
for an arbitrary
continuous random variable X.
(b)
Evaluate the mean and variance if X is a Laplacian random variable with
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 Spring '11
 Prof.ShenghuiSong
 Probability theory

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