Let
be a sample (size n=1) from the exponential distribution, which has
the pdf
, where
is an unknown
parameter. Let's define a statistic as
.
Is
a sufficient
statistic for
?
Homework Answers
Add Answer to:
Let
be a sample (size n=1) from the exponential distribution, which has
the pdf
, where...
Let be a sample (size n = 1) from the exponential distribution, which has the pdf...
Let be a sample (size n = 1) from the exponential distribution, which has the pdf where is an unknown parameter. Let's define a statistic as . Is a sufficient statistic for ? We were unable to transcribe this imagef(x: λ) = Xe We were unable to transcribe this imageT(X) = 11>2 T(X) We were unable to transcribe this image
Let X1, X2, ..., Xn be a random sample from X which has pdf depending on...
Let X1, X2, ..., Xn be a random
sample from X which has pdf
depending on a parameter
and
(i)
(ii)
where
< x <
. In both these two cases
a) write down the log-likelihood function and find a
1-dimensional sufficient statistic for
b) find the score function and the maximum likelihood estimator
of
c) find the observed information and evaluate the Fisher
information at
= 1.
f(20) We were unable to transcribe this image((z(0 – 2) - )dxəz(47)...
Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...
Let X1, X2,.......Xn be a
random sample of size n from a continuous distribution symmetric
about .
For testing H0: =
10 vs H1: <
10, consider the statistic T- =
Ri+ (1-i),
where i
=1 if Xi>10 , 0 otherwise; and
Ri+ is the rank of (Xi - 10) among
|X1 -10|, |X2-10|......|Xn
-10|.
1. Find the null mean and variance of T- .
2. Find the exact null distribution of T- for
n=5.
We were unable to transcribe this imageWe were...
Let be a random sample from , where is an unknown parameter. Show that is a...
Let be a random sample from , where is an unknown parameter. Show that is a sufficient statistics for , where is the sample variance. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image2 We were unable to transcribe this imageWe were unable to transcribe this image
Suppose n independent, identically distributed observations are drawn from an exponential () distribution, with pdf given...
Suppose n independent, identically distributed observations are
drawn from an exponential ()
distribution, with pdf given by f(x,)=,
0 < x <
.
The data are x1, x2, .. , xn
Construct a likelihood ratio hypothesis test of Ho :
vs H1:
(where
and
are known constants, with
), where the critical value is taken to be a constant c
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were...
Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs...
Independent random samples X1, X2, . . . , Xn are from
exponential distribution with pdfs
, xi > 0, where λ is fixed but unknown. Let
. Here we have a relative large sample size n = 100.
(ii) Notice that the population mean here is µ = E(X1) = 1/λ ,
population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the
sample standard deviation s = 10, sample average
= 5, construct a 95% large-sample approximate confidence...
Let X1, X2, X3 ∼(iid) Exponential(λ). (a) Show that T(X1, X2, X3) = X1 + X2...
Let X1, X2, X3 ∼(iid) Exponential(λ).
(a) Show that T(X1, X2, X3) = X1 + X2 + X3 is a sufficient
statistic for λ.
(b) Find the MVUE for λ.
(c) Show that
is not a sufficient statistic for λ.
(d) Let
=
and find
. Give an argument for why
is not the best estimator of λ.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
3. Let ,..., be independent random sample from N(), where is unknown. (i) Find a sufficient...
3. Let ,..., be
independent random sample from N(),
where is unknown.
(i) Find a sufficient statistic of .
(ii) Find the MLE of .
(iii) Find a pivotal quantity and use it to construct a
100(1–)% confidence
interval for .
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
Let denote the sample mean of an independent random sample of size 25 from the distribution...
Let denote the sample mean of an independent random sample of size 25 from the distribution whose p.d.f. is , 0 < x < 2. Find an approximation of P(1.3 < < 1.6). We were unable to transcribe this imagef (x)- We were unable to transcribe this image
Let {} be a random sample from the distribution. (a) Find a sufficient statistic for when...
Let {} be a random sample from the distribution. (a) Find a sufficient statistic for when is known (b) Find a sufficient statistic for when is known 7l beta ( α , β ) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let X1, X2, ..., Xn be a random
sample from X which has pdf
depending on a parameter
and
(i)
(ii)
where
< x <
. In both these two cases
a) write down the log-likelihood function and find a
1-dimensional sufficient statistic for
b) find the score function and the maximum likelihood estimator
of
c) find the observed information and evaluate the Fisher
information at
= 1.
f(20) We were unable to transcribe this image((z(0 – 2) - )dxəz(47)...
Let X1, X2,.......Xn be a
random sample of size n from a continuous distribution symmetric
about .
For testing H0: =
10 vs H1: <
10, consider the statistic T- =
Ri+ (1-i),
where i
=1 if Xi>10 , 0 otherwise; and
Ri+ is the rank of (Xi - 10) among
|X1 -10|, |X2-10|......|Xn
-10|.
1. Find the null mean and variance of T- .
2. Find the exact null distribution of T- for
n=5.
We were unable to transcribe this imageWe were...
Suppose n independent, identically distributed observations are
drawn from an exponential ()
distribution, with pdf given by f(x,)=,
0 < x <
.
The data are x1, x2, .. , xn
Construct a likelihood ratio hypothesis test of Ho :
vs H1:
(where
and
are known constants, with
), where the critical value is taken to be a constant c
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were...
Independent random samples X1, X2, . . . , Xn are from
exponential distribution with pdfs
, xi > 0, where λ is fixed but unknown. Let
. Here we have a relative large sample size n = 100.
(ii) Notice that the population mean here is µ = E(X1) = 1/λ ,
population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the
sample standard deviation s = 10, sample average
= 5, construct a 95% large-sample approximate confidence...
Let X1, X2, X3 ∼(iid) Exponential(λ).
(a) Show that T(X1, X2, X3) = X1 + X2 + X3 is a sufficient
statistic for λ.
(b) Find the MVUE for λ.
(c) Show that
is not a sufficient statistic for λ.
(d) Let
=
and find
. Give an argument for why
is not the best estimator of λ.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
3. Let ,..., be
independent random sample from N(),
where is unknown.
(i) Find a sufficient statistic of .
(ii) Find the MLE of .
(iii) Find a pivotal quantity and use it to construct a
100(1–)% confidence
interval for .
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
Most questions answered within 3 hours.
-
A 1.5 m long string is tied between two posts. what is the
wavelength of the...
asked 16 seconds ago -
The personnel office at a large electronics firm regularly
schedules job interviews and maintains records of...
asked 8 minutes ago -
Determine the P-value for this hypothesis test. (Round to the
nearest three decimal places as needed)...
asked 50 minutes ago -
A manufacturer of banana chips would like to know whether its
bag filling machine works correctly...
asked 1 hour ago -
According to an airline, flights on a certain route are on time
85% of the time....
asked 1 hour ago -
Calculate the pH of a buffer solution made with 0.75 M
HC2H3O2 and 0.25 M
NaC2H3O2...
asked 13 minutes ago -
A manufacturer of medical supplies provides the following
partial financial information:
Total fixed costs: $35,000
Unit...
asked 12 minutes ago -
A small business ships specialty homemade candies to anywhere in
the world. Past records indicate that...
asked 47 minutes ago -
The rate at which a certain drug is eliminated by the body
follows first-order kinetics, with...
asked 39 minutes ago -
For a given population, the percentage of full-time employees
that participate in a retirement plan is...
asked 1 hour ago -
Explain at least two other important functions of auxin in
plants besides gravitropism and phototropism.
asked 19 minutes ago -
How much heat is required to heat 2.79 grams of ice to 125C?
And can you...
asked 29 minutes ago