Suppose
constitute a random sample drawn from a population N(
,
)
and
constitute a random sample drawn from another population
N(
,
).
The two samples are drawn independently. Derive a generalised
likelihood ratio test for testing
against
where
and
are
positive constants such that
>
.
Suppose constitute a random sample drawn from a population N(, ) and constitute a random samp...
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
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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.
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Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test for testing Ho : μ Ho versus H! : μ where μ. μο. 123. (5 points)
Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test...
A random sample of communities in
certain state gave the following information for people under 25
years of age.
x1: Rate of hay fever per 1000 population
for people under 25
A random sample of regions in
certain state gave the following information for people over 50
years old.
x2: Rate of hay fever per 1000 population
for people over 50
Assume that the hay fever rate in each age group has an
approximately...
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 .
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POINT ESTIMATION Let be a simple random sample of a population , with , and let be a known integer , . Find the MVUE ( minimum-variance unbiased estimator ) for the function of : Thank you for the explanations. X1, X2,..,X n Ber (0 E (0, 1) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imaged (0) -s (1 - 0)" X1, X2,..,X n Ber (0 E (0, 1)...
Let X1, X2, ..., Xn be a random sample of size n from the
distribution with probability density function
To answer this question, enter you answer as a formula. In
addition to the usual guidelines, two more instructions for this
problem only : write
as single variable p and
as m. and these can be used as inputs of functions as usual
variables e.g log(p), m^2, exp(m) etc. Remember p represents the
product of
s only, but will not work...
To test H0: σ= 2.3 versus H1 : σ> 2.3, a random sample of size n = 18 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d). (a) If the sample standard deviation is determined to be s- 2.1, compute the test statistic. z(Round to three decimal places as needed,) TO test H0: ơ-1.4 versus H1 : ơt 1.4, a random sample of size n-21 is obtained from a population that is...
Let X, X,, ..., X, denote a random sample of size n from a population with pdf (10) = b exp(@m()).0<x<1 where (<O<0. Derive that the likelihood ratio test of H.:0=1 versus H, :0 #1 in terms of T(x) = ŽI (3)
Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj) . 1. Find v so that P[V>=v]=0.45 when 1=2. 2. Find the mean and variance of V when 1=2. 10 10 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...