Question

how would you use the Cholesky factorization to obtain an IID sample of size n from the Np(c,Σ) distribution?

Answer #1

ANSWER:

Prove that for a sample of n where Xi ~ iid Bernoulli
(p) and Yn = ∑Xi, that
Bn
= [Yn
– np] / √[np(1-p)] -->D N(0,1)
i.e. Bn has a limiting distribution of the standard
normal. No need to use the MGF, you can use a theorem to answer
this (which you must identify). Show all steps and parameterize the
RV as the theorem specifies

Suppose a simple random sample of size n+75 is obtained from a
population whose size is N=10,000 and whose population proportion
with a specified characteristic is p= 0.6 . Complete parts (a)
through (c) below.
(a) Describe the sampling distribution of p^. Choose the phrase
that best describes the shape of the sampling distribution
below.
A.) Not normal because n<_ 0.05N and np(1-p)<10.
B.) Approximately normal because n<_0.05N and
np(1-p)>_10.
C). Not normal because n<_0.05N and np(1 -p)>_10.
D). Approximately...

Show that the sum of the observations of a random sample of size
n from
a gamma distribution that has pdf f(x; θ) = (1/θ)e^(−x/θ), 0 < x
< ∞, 0 < θ < ∞,
zero elsewhere, is a sufficient statistic for θ. Use Neyman's
Factorization Theorem.

Let X1, X2, . . . , Xn be a random sample of size n from a
distribution with variance σ^2. Let S^2 be the sample variance.
Show that E(S^2)=σ^2.

You want to obtain a sample to estimate a population mean. Based
on previous evidence, you believe the population standard deviation
is approximately σ=59.2. You would like to be 98% confident that
your estimate is within 10 of the true population mean. How large
of a sample size is required?
n = __________________

You want to obtain a sample to estimate a population mean. Based
on previous evidence, you believe the population standard deviation
is approximately σ=72.7. You would like to be 99% confident that
your esimate is within 3 of the true population mean. How large of
a sample size is required?
n =

You want to obtain a sample to estimate a population mean. Based
on previous evidence, you believe the population standard deviation
is approximately σ = 63.5 . You would like to be 98% confident that
your estimate is within 4 of the true population mean. How large of
a sample size is required? n = ?

You want to obtain a sample to estimate a population mean. Based
on previous evidence, you believe the population standard deviation
is approximately σ=77.3. You would like to be 99% confident that
your esimate is within 1 of the true population mean. How large of
a sample size is required?
n =

You want to obtain a sample to estimate a population mean. Based
on previous evidence, you believe the population standard deviation
is approximately σ = 56.5 . You would like to be 98% confident that
your esimate is within 4 of the true population mean. How large of
a sample size is required?
n =

You want to obtain a sample to estimate a population mean. Based
on previous evidence, you believe the population standard deviation
is approximately σ=75.4σ=75.4. You would like to be 95% confident
that your estimate is within 5 of the true population mean. How
large of a sample size is required? n=____

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 11 minutes ago

asked 19 minutes ago

asked 21 minutes ago

asked 22 minutes ago

asked 36 minutes ago

asked 44 minutes ago

asked 46 minutes ago

asked 49 minutes ago

asked 49 minutes ago

asked 50 minutes ago

asked 1 hour ago