This preview shows pages 1–2. Sign up to view the full content.
Fall 2008
Test III
Page: 1 of 2
Introduction to Probability
Monday, October 27, 2008
STA 4321/5325
Instructions:
Please turn of your cell phones. Please write
all
oF your answers on a separate sheet oF
paper and make sure you have clearly labeled the problem corresponding to your answer. Absolutely no
cheating. This test has a total oF 55 points.
Name:
Some Equations
Poisson
If
X
∼
Pois(
λ
), the pmf of
X
is
p
(
x
)=
λ
x
x
!
e

λ
Hypergeometric
If
X
∼
hypergeom(
N,k,n
), the pmf of
X
is
p
(
x
)=
(
k
x
)(
N

k
n

x
)
(
N
n
)
and E(
X
)=
nk/N
.
Exponential
If
X
∼
exp(
θ
), the pdf of
X
is
f
(
x
)=
±
1
θ
e

x/θ
,x
≥
0
0
,
else
Gamma
If
X
∼
gamma(
α, β
), the pdf of
X
is
f
(
x
)=
±
1
Γ(
α
)
β
α
x
α

1
e

x/β
,x
≥
0
0
,
else
Also, E(
X
)=
αβ
and var(
X
)=
αβ
2
.
◦
1
(3+4=7 points) Suppose that 60% of the toasters produced for Target are defective. If toasters are
randomly purchased one at a time, ±nd the probability that:
(a) Exactly two defective toasters are bought before a working toaster is bought.
(b) At least two defective toasters are bought before the second working toaster is bought.
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.
 Fall '08
 Staff
 Probability

Click to edit the document details