Question
In: Statistics and Probability
*Daily presentation for Friday, January 31*: Suppose we have a random sample from a Bernoulli(p) distribution....
*Daily presentation for Friday, January 31*:
Suppose we have a random sample from a Bernoulli(p)
distribution. Show that the MoM using E[X] is nice and simple,
while the MoM using Var[X] is complex and weird.
Solutions
orchestra answered 2 years agoRelated Solutions
Let X1,..., Xn be a random sample from the Bernoulli distribution: Use the likelihood ratio test...
Let X1,..., Xn be a random sample from the Bernoulli
distribution:
Use the likelihood ratio test to give a form of test (without
specifying the value of the critical value) for H0: p= 1 versus
H1:p ≠1.
For this question assume that we have a random sample from a normal distribution with unknown...
For this question assume that we have a random sample from a
normal distribution with
unknown mean but known variance.
(a) Suppose that we have 36 observations, the sample mean is 5,
and the population
variance is 9. Construct a 95% confidence interval for the
population mean.
(b) Repeat the preceding with a population variance of 25 rather
than 9.
(c) Repeat the preceding with a sample size of 25 rather than
36.
(d) Repeat the preceding but construct a...
We have a random sample of size 10 from a normal distribution. We wish to estimate...
We have a random sample of size 10 from a normal distribution.
We wish to estimate the population mean. Damjan suggests taking the
average of the sample minimum and sample maximum. Allan thinks this
will be a poor estimator and says we should use the sample mean
instead. Do a simulation in R to compare these two
estimators in terms of their bias and variance. Include a
side-by-side boxplot that compares their sampling
distributions.
We have a random sample of size 10 from a normal distribution. We wish to estimate...
We have a random sample of size 10 from a normal distribution.
We wish to estimate the population mean. joseph suggests taking the
average of the sample minimum and sample maximum.steve thinks this
will be a poor estimator and says we should use the sample mean
instead. Do a simulation in R to compare these two estimators in
terms of their bias and variance. Include a side-by-side boxplot
that compares their sampling distribut
showing R output also
Let Y1,Y2,...,Yn be a Bernoulli distributed random sample with P(Yi = 1) = p and P(Yi...
Let Y1,Y2,...,Yn be a Bernoulli distributed random sample with
P(Yi = 1) = p and P(Yi = 0) = 1−p for all i.
(a) Prove that E(¯ Y ) = p and V (¯ Y ) = p(1−p)/n2, for the
sample mean ¯ Y of Y1,Y2,...,Yn, and find a sufficient statistic U
for p and show it is sufficient for p.
(b) Find MVUE for p and show it is unbiased for p.
Suppose, for a random sample selected from a normal population, we have the values of the...
Suppose, for a random sample selected from a normal population,
we
have the values of the sample mean x ̄ = 67.95 and the standard
deviation s = 9.
a. Construct a 95% confidence interval for population mean μ
assuming the sample size n = 16.
b. Construct a 90% confidence interval for population mean μ
assuming n = 16.
c. Obtain the width of the confidence intervals calculated in a and
b. Is the width of 90% confidence
interval...
Suppose that ?!,···, ?" form a random sample from the beta distribution with parameters ? and...
Suppose that ?!,···, ?" form a random sample from the beta
distribution with parameters ? and
?. Find the moments estimators for ? and ?.
NOTE: Please make the solution as well detailed as possible
especially the making of ? and
? the subject of formular respectively
Suppose you have selected a random sample of ?=13 measurements from a normal distribution. Compare the...
Suppose you have selected a random sample of ?=13 measurements
from a normal distribution. Compare the standard normal z values
with the corresponding t values if you were forming the following
confidence intervals.
a) 80% confidence interval
?=
?=
(b) 90% confidence interval
?=
?=
(c) 99% confidence interval
?=
?=
Sampling distribution question State the definition of sampling distribution? Let’s assume that we have a Bernoulli...
Sampling distribution question
State the definition of sampling distribution?
Let’s assume that we have a Bernoulli random variable X,
X = a with probability 0.78,
X = b with probability
0.22,
Where a and b are the third and fourth
digit of your student number, respectively.(a=9,b=9) Develop a
sampling distribution for sample means of the Bernoulli
distribution when the sample size is 6
What is the expected value of sample means in question 3.b?
What is the variance of the...
Suppose we wish to generate a sample from the exponential ($\beta$) distribution, and only have access...
Suppose we wish to generate a sample from the exponential
($\beta$) distribution, and only have access to a computer which
generates numbers from the skew logistic distribution. It turns out
that if $X$~SkewLogistic ($\beta$), then log(1+exp($-X$)) is
exponential ($\beta$). Show that this is true and check by
simulation that this transformation is correct.
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