Homework 3 (Chapter 4) Due Wednesday, June 15
1. Given the number of heads obtained in three tosses of a fair coin, find the corresponding
events and probability for each value of X.
(6 points)
2. Are the following functions probability distributions? Why or why not?
(6 points)
(a)
2
2
)
(

=
x
x
f
for
4
,
3
,
2
,
1
=
x
(b)
25
)
(
2
x
x
f
=
for
4
,
3
,
2
,
1
,
0
=
x
①
f(x)≥0
(a) f(x
1
)=1/2
(b)∑f(x)≠1
②
∑f(x)=1
both (a) and (b) are NOT probability distributions.
3. 30% of the trees in a forest are infested with a parasite. Four trees are selected at random. X:
number of trees sampled that have the parasite. Let I: infested, N: not infested. Find the
probability and cumulative probability for each value of X.
(6 points)
4. Given the following distribution,
find the mean and the variance.
(9
Points)
Outcome
X
HHH
3
HHT
2
HTH
2
HTT
1
THH
2
THT
1
TTH
1
TTT
0
Value of
X
P(X=x)
F(x)
0
(.3)
0
(.7)
4
=.2401
.2401
1
4(.3)(.7)
3
=.4116
.6517
2
6(.3)
2
(.7)
2
=.2646
.9163
3
4(.3)
3
(.7)
1
=.0756
.9919
4
0
4
1
x
f(x)
xf(x)
(xµ)²
(xµ)²f(x)
1
.4
.4
9
3.6
2
.1
.2
4
.4
6
.3
1.8
4
1.2
8
.2
1.6
16
3.2
Total
1
(µ)=4
33
(σ²)=8.4
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 Summer '08
 Mendell
 Normal Distribution, Probability, Probability distribution, Probability theory, Cumulative distribution function

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