UCSD ECE 153
Handout #7
Prof. YoungHan Kim
Thursday, October 9, 2008
Homework Set #2
Due: Thursday, October 16, 2008
1. Read Sections 3.1–3.2, 3.4–3.6, 4.1–4.2, 4.4–4.5, 4.7, 4.9, 5.15.5, 5.75.8 in the text.
Try to work on all examples.
2.
Juror’s fallacy.
Suppose that
P
(
A

B
)
≥
P
(
A
) and
P
(
A

C
)
≥
P
(
A
). Is it always true
that
P
(
A

B, C
)
≥
P
(
A
) ? Prove or provide a counterexample.
3. Let
X
be a geometric random variable with pmf
p
X
(
k
) =
p
(1

p
)
k

1
, k
= 1
,
2
, . . . .
Find and plot the conditional pmf
p
X
(
k

A
) =
P
{
X
=
k

X
∈
A
}
if:
(a)
A
=
{
X > m
}
where
m
is a positive integer.
(b)
A
=
{
X < m
}
.
(c)
A
=
{
X
is an even number
}
.
Comment on the shape of the conditional pmf of part (a).
4.
Negative binomial.
Suppose we observe an inﬁnite sequence of independent coin ﬂips
with bias
p
(i.e., the probability of heads is
p
each time). Let
X
be the number of coin
ﬂips until observing
k
heads. Find the pmf of the random variable
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '09
 Eggers
 Probability theory, Alice, Discrete probability distribution, Prof. YoungHan Kim

Click to edit the document details