Covariance of multinomial random variables,

pedzenekO
2021-01-19
Answered

To know:Distribution of the sum of multinomial random variables.

Covariance of multinomial random variables,

$COV({N}_{i},{N}_{j})=-m{P}_{i}{P}_{j},$

Covariance of multinomial random variables,

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berggansS

Answered 2021-01-20
Author has **91** answers

For obtaining the result, we could have used

We have

Such that

Rewrite the above

Thus,

With parameters m and

The distribution of the sum of multinomial random variables is Binomial.

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Consider the following:

1. Test for significance of the coefficient of determination

2. F-test for overall model significance

3. Test for significance of the slope coefficient

4. Test for significance of the correlation coefficient

Assuming you have a 5% level of significance, which of the above give equivalent conclusions a simple linear regression?

Select one:

a. 1, 2 and 3

b. 2 and 3

c. 1, 2, 3, and 4

d. 2, 3, and 4

e. 2 and 4

1. Test for significance of the coefficient of determination

2. F-test for overall model significance

3. Test for significance of the slope coefficient

4. Test for significance of the correlation coefficient

Assuming you have a 5% level of significance, which of the above give equivalent conclusions a simple linear regression?

Select one:

a. 1, 2 and 3

b. 2 and 3

c. 1, 2, 3, and 4

d. 2, 3, and 4

e. 2 and 4

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Let $\mathcal{X}$ be a sample space, $T$ a test statistic and $G$ be a finite group of transformations (with M elements) from $\mathcal{X}$ onto itself. Under the null-hypothesis the distribution of the random variable $X$ is invariant under the transformations in $G$. Let

$\hat{p}=\frac{1}{M}\sum _{g\in G}{I}_{\{T(gX)\ge T(X)\}}.$

Show that $P(\hat{p}\le u)\le u$ for $0\le u\le 1$ under the null hypothesis

$\hat{p}=\frac{1}{M}\sum _{g\in G}{I}_{\{T(gX)\ge T(X)\}}.$

Show that $P(\hat{p}\le u)\le u$ for $0\le u\le 1$ under the null hypothesis

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Answer true or false to each of the statements in parts (a) and (b), and explain your reasoning.
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