C
OMER
ECE 600 Homework 2
1.
Let A and B be two events in a probability space.
a.
Show that if A and B are independent, then A
c
and B are also independent.
b.
If A and B are independent, are they mutually exclusive? Explain.
c.
Show that if P(AB) > P(A), then P(BA) > P(B).
2.
If A, B, and C are events in a probability space, show that P(A
°
B
°
C) =
P(AB
°
C)P(BC)P(C).
3.
An experiment consists of picking one of two urns at random, with the two urns
being equally likely, and then selecting a ball from the urn and noting its color
(black or white). Let A be the event “urn 1 is selected” and B the event “a black
ball is selected.” Under what conditions are the events A and B independent?
4.
There are two servers at the gorcery store. Server 1 can take anywhere from 1 to
5 minutes to complete an order. Server 2 can take anywhere from 1 to 10 minutes
to complete an order. Let T
S
denote the service time. You are given that
°
°
±
°
°
²
³
>
≤
<

≤
=
≤
5
,
1
5
1
,
4
1
1
,
0
1)
Server

P(T
S
t
t
t
t
t
°
°
±
°
°
²
³
>
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 Fall '08
 Staff
 Probability, Probability theory, Probability space, TS

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