Let X1, ..., Xn be a random sample from a uniform distribution on [0, 0]. Let the point estimator to be 433 35,923 n+1 Ô max{X1, ..., Xn}. n Show that the pdf of Y = max{X1, ..., Xn} is fr (y; 0) = { nyn - 1/07, 0 ≤ y ≤o 0, otherwise (Hints: find the cdf of Y first) b) Show that the point estimator Ô is unbiased for 0. c) The random variable U = Y/O has the density function: nun-1, 0≤u≤1 unu } = . fu(u) = 0, otherwise C Use fu(u) to verify that 1/n Y P((2)³/ < / ≤ (1-2)³/") = 1 and use this to derive a 100(1-a)% CI for 0. 1/n = 1-a Verify that P (a¹/<< 1) = 1 - α, and derive a 100(1-a)% CI for based on this probability statement. Which of the two intervals derived previously is shorter? If my waiting time for a morning bus is uniformly distributed and observed waiting times are x₁ = 4.2, x2 = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4, derive a 95% CI for by using the shorter of the two intervals. d) e) zoom 18 MacBook Pro $ G Search or type URL % do LO 5 Λ > 6 & ≈ 7 ±4 #3 3 LLI E R T Y כ * 8 6 0
Let X1, ..., Xn be a random sample from a uniform distribution on [0, 0]. Let the point estimator to be 433 35,923 n+1 Ô max{X1, ..., Xn}. n Show that the pdf of Y = max{X1, ..., Xn} is fr (y; 0) = { nyn - 1/07, 0 ≤ y ≤o 0, otherwise (Hints: find the cdf of Y first) b) Show that the point estimator Ô is unbiased for 0. c) The random variable U = Y/O has the density function: nun-1, 0≤u≤1 unu } = . fu(u) = 0, otherwise C Use fu(u) to verify that 1/n Y P((2)³/ < / ≤ (1-2)³/") = 1 and use this to derive a 100(1-a)% CI for 0. 1/n = 1-a Verify that P (a¹/<< 1) = 1 - α, and derive a 100(1-a)% CI for based on this probability statement. Which of the two intervals derived previously is shorter? If my waiting time for a morning bus is uniformly distributed and observed waiting times are x₁ = 4.2, x2 = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4, derive a 95% CI for by using the shorter of the two intervals. d) e) zoom 18 MacBook Pro $ G Search or type URL % do LO 5 Λ > 6 & ≈ 7 ±4 #3 3 LLI E R T Y כ * 8 6 0
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
Related questions
Question
Stats and probability
![Let X1, ..., Xn be a random sample from a uniform distribution on [0, 0]. Let the point
estimator to be
433
35,923
n+1
Ô
max{X1, ..., Xn}.
n
Show that the pdf of Y = max{X1, ..., Xn} is
fr (y; 0) = { nyn - 1/07, 0 ≤ y ≤o
0, otherwise
(Hints: find the cdf of Y first)
b)
Show that the point estimator Ô is unbiased for 0.
c)
The random variable U = Y/O has the density function:
nun-1, 0≤u≤1
unu } = .
fu(u) =
0, otherwise
C
Use fu(u) to verify that
1/n Y
P((2)³/ < / ≤ (1-2)³/") = 1
and use this to derive a 100(1-a)% CI for 0.
1/n
= 1-a
Verify that P (a¹/<< 1) = 1 - α, and derive a 100(1-a)% CI for
based on this probability statement.
Which of the two intervals derived previously is shorter? If my waiting time
for a morning bus is uniformly distributed and observed waiting times are x₁ = 4.2,
x2 = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4, derive a 95% CI for by using the shorter
of the two intervals.
d)
e)
zoom
18
MacBook Pro
$
G Search or type URL
%
do LO
5
Λ
>
6
&
≈ 7
±4
#3
3
LLI
E
R
T
Y
כ
*
8
6
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa79c18d0-6a0e-4a38-9496-04f82bd62d69%2Faf40a494-a7b1-4691-a53e-98a18fe852b1%2Fway6pg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X1, ..., Xn be a random sample from a uniform distribution on [0, 0]. Let the point
estimator to be
433
35,923
n+1
Ô
max{X1, ..., Xn}.
n
Show that the pdf of Y = max{X1, ..., Xn} is
fr (y; 0) = { nyn - 1/07, 0 ≤ y ≤o
0, otherwise
(Hints: find the cdf of Y first)
b)
Show that the point estimator Ô is unbiased for 0.
c)
The random variable U = Y/O has the density function:
nun-1, 0≤u≤1
unu } = .
fu(u) =
0, otherwise
C
Use fu(u) to verify that
1/n Y
P((2)³/ < / ≤ (1-2)³/") = 1
and use this to derive a 100(1-a)% CI for 0.
1/n
= 1-a
Verify that P (a¹/<< 1) = 1 - α, and derive a 100(1-a)% CI for
based on this probability statement.
Which of the two intervals derived previously is shorter? If my waiting time
for a morning bus is uniformly distributed and observed waiting times are x₁ = 4.2,
x2 = 3.5, x3 = 1.7, x4 = 1.2, and x5 = 2.4, derive a 95% CI for by using the shorter
of the two intervals.
d)
e)
zoom
18
MacBook Pro
$
G Search or type URL
%
do LO
5
Λ
>
6
&
≈ 7
±4
#3
3
LLI
E
R
T
Y
כ
*
8
6
0
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