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Unformatted text preview: ELEC210 Spring 2011 Homework 6
1. Let X and Y have joint pdf:
()
(a) Find ( ).
(b) Find
.
(c) Find
using part b.
(d) Find
.
2. A message requires N time units to be transmitted, where N is a geometric
(
)
random variable with pmf
A single new message
arrives during a time unit with probability , and no messages arrive with
probability
. Let K be the number of new messages that arrive during the
transmission of a single message.
(a) Find
and
using conditional expectation.
(b) Find the pmf of . Hint: ( ) ( ) ∑ () . 3. The number X of goals the Bulldogs score against the Flames has a geometric
distribution with mean 2; the number of goals Y that the Flames score against
the Bulldogs is also geometrically distributed but with mean 4.
(a) Find the pmf of
. Assume X and Y are independent.
(b) What is the probability that the Bulldogs beat the Flames? Tie the Flames?
(c) Find
.
4. Let X and Y be independent random variables that are uniformly distributed in
the interval
. Find the pdf of
.
5. Let X, Y, Z have joint pdf:
(
)
(
)
(a) Find k.
(b) Find (
) and (
).
(c) Find ( ) ( ) and ( ).
(d) Find the mean vector and covariance matrix for ( ). ...
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This note was uploaded on 10/16/2011 for the course ELEC 308,315,10 taught by Professor Prof.shenghuisong during the Spring '11 term at CUHK.
 Spring '11
 Prof.ShenghuiSong

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