This preview shows pages 1–2. Sign up to view the full content.
STAT 410
Summer 2009
Homework #5
(due Friday, July 10, by 4:00 p.m.)
1.
Let
X
and
Y
be independent random variables, each geometrically distributed
with the probability of “success”
p
,
0 <
p
< 1.
That is,
p
X
(
k
) =
p
Y
(
k
) =
( 29
1
1


⋅
k
p
p
,
k
= 1, 2, 3, … ,
a)
Find
P
(
X
> Y
).
[ Hint:
You may find it helpful to find
P
(
X = Y
)
first.
]
b)
Find
P
(
X
+ Y =
n
),
n
= 2, 3, 4, …
,
and
P
(
X =
k

X
+ Y =
n
),
k
= 1, 2, 3, … ,
n
– 1.
2.
Suppose the size of largemouth bass in a particular lake is uniformly distributed
over the interval 0 to 8 pounds.
A fisherman catches (a random sample of) 5 fish.
a)
What is the probability that the smallest fish weighs less than 2 pounds?
b)
What is the probability that the largest fish weighs over 7 pounds?
c)
What is the probability that the largest fish weighs between 6 and 7 pounds?
d)
What is the probability that the second largest (fourth smallest) fish weighs
between 4 and 6 pounds?
3.
Three actuaries are independently hired to appraise the value of a company.
The true
value of the company is
θ
million dollars, and each actuary’s estimate is uniformly
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.
 Spring '08
 STEPANOV
 Statistics, Probability

Click to edit the document details