What type of correlation is the graph below?

Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/

Burka [1]

Answer:

The answer is " $\bold{\frac{2}{n}}$ ".

Step-by-step explanation:

considering $Y_1, Y_2,........, Y_n$ signify a random Poisson distribution of the sample size of n which means is λ.

$E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda$

Let assume that,

$\hat \lambda_i = \frac{Y_1+Y_2}{2}$

multiply the above value by Var on both sides:

$Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )$

$=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\$

now consider $\hat \lambda_2$ = $\bar Y$

$Var (\hat \lambda_2 )= Var(\bar Y )$

$=Var \{ \frac{\sum Y_i}{n}\}$

$=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\$

For calculating the efficiency divides the $\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2$ value:

Formula:

$\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}$

$=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}$

8 0

3 years ago

Trig help please, 2 questions, 10 pts

Scrat [10]

1. 2700 degrees. 450 rotations in on minute is 450(360) degrees per minute. If you divide this by 60 you get 2700.
2. 180 degrees. 4.3 rotations per minute is 4.3 times 360 degrees per minute. Multiply that times 5, and divide the answer by 360 and you get 21.5, which means he is 180 degrees from his starting point.

4 0

3 years ago

If AB = DE CA = FD angle B is congruent to angle E angle A is congruent to angle D , then ∆ABC and ∆DEF are congruent by the ASA

bonufazy [111]

What is f congruebt to i think it is congruent

3 0

4 years ago

Please help asap find f -1

ExtremeBDS [4]

I.
Given a function f with domain D and range R, and the inverse function
$f ^{-1}$ ,

then the domain of $f ^{-1}$ is the range of f, and the range of $f ^{-1}$ is the domain of f.

II. We are given the function $f(x)= \sqrt{x-5}$ ,

the domain of f, is the set of all x for which $\sqrt{x-5}$ makes sense, so x is any x for which x-5 $\geq$ 0, that is x≥5.

the range is the set of all values that f can take. Since f is a radical function, it never produces negative values, in fact in can produce any value ≥0

Thus the Domain of f is [5, ∞) and the Range is [0, ∞)
then , the Domain of $f ^{-1}$ is [0, ∞) and the Range of $f ^{-1}$ is [5, ∞)

III.
Consider $f(x)= \sqrt{x-5}$

to find the inverse function $f^{-1}$ ,

1. write f(x) as y:

$y= \sqrt{x-5}$

2. write x in terms of y:

$y= \sqrt{x-5}$

take the square of both sides

$y^{2} =x-5$

add 5 to both sides

$y^{2} +5=x$

$x=y^{2} +5$

3. substitute y with x, and x with $f^{-1}(x)$ :

$f^{-1}(x)=x^{2} +5$

These steps can be applied any time we want to find the inverse function.

IV. Answer:

$f^{-1}(x)=x^{2} +5$ , x≥0

y≥0, where y are all the values that $f^{-1}$ can take

Remark: the closest choice is B

8 0

3 years ago

What type of chart essentially adds a third dimension

Jet001 [13]

The Bubble Charts that the answer

4 0

4 years ago

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