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Do My Statistics Homework

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Types of Statistics Academic Papers We Can Write

Statistics term papers

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Statistics research papers

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Theses and dissertations are more comprehensive academic papers that provide detailed analyses of the statistics topics through different research techniques. Our statistics homework helpers can help you write different parts of your statistics theses and dissertations, including literature review, methodology, findings, and analysis.

Statistical projects

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Basic knowledge of online college statistics can help you during your studies. Most students worry about their statistics project and how they can pass their college statistics homework.

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Stay calm and study hard.

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If you find it challenging to pass basic courses with minimal effort, statistics homework will be a challenge.

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Sample Math homework statistics questions from our experts

Q: If X is a random variable with X normally distributed. Let x bar be a random sample of size n and z = square root n times xbar - mean / standard deviation, which of the following is true due to CLT?

Answer

Let X1, X2,..., XnX1, X2,..., Xn be a random sample from X∼N(μ,σ2). X∼N(μ,σ2).
Now let X¯=1n∑ni=1XiX¯=1n∑i=1nXi,
and Z=n−−√X¯−μσ.Z=nX¯−μσ.

What is the distribution of X¯X¯?

A linear combination of normally distributed variables is also normally distributed.
X¯∼N(E[X¯], V[X¯])X¯∼N(E[X¯], V[X¯]),
where
E[X¯]=...=μE[X¯]=...=μ
V[X¯]=...=σ2/nV[X¯]=...=σ2/n.

What is the distribution of ZZ?

ZZ is a linear combination of normally distributed variables and is thus normally distributed itself. Z∼N(E[Z],V[Z])Z∼N(E[Z],V[Z]),
where
E[Z]=...=0E[Z]=...=0
V[Z]=...=1.V[Z]=...=1.

Which holds for any sample size nn.

What about CLT, then?

Above, the stochastic variable XX is normally distributed, and any linear combination of normally distributed variables is also normally distributed. However, what happens if XX is not normally distributed?
Suppose that X1,...,XnX1,...,Xn is a random sample (i.i.d) from an unknown distribution with mean E[X]=μE[X]=μ and variance V[X]=σ2<∞V[X]=σ2<∞. Then as nn approaches infinity, n−−√(X¯−μ)n(X¯−μ) converges in distribution to a normal

N(0,σ2)N(0,σ2) :

Z=n−−√X¯−μσ−→d.N(0,1)Z=nX¯−μσ→d.N(0,1),
as n→∞n→∞.

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Frequently Asked Questions

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