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3 years ago

What is this "√", called?

2 answers:

8 0

A Square Root is something you would in mathmatics. Like the square root of 49 is 7. Its just doubles 7x7 equal 49. 8x8 is 64 so the square root of 64 is 8.

Katyanochek1 [597]3 years ago

6 0

That is called square root

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Let X1 and X2 be independent random variables with mean μand variance σ².

My name is Ann [436]

Answer:

a) $E(\hat \theta_1) =\frac{1}{2} [E(X_1) +E(X_2)]= \frac{1}{2} [\mu + \mu] = \mu$

So then we conclude that $\hat \theta_1$ is an unbiased estimator of $\mu$

$E(\hat \theta_2) =\frac{1}{4} [E(X_1) +3E(X_2)]= \frac{1}{4} [\mu + 3\mu] = \mu$

So then we conclude that $\hat \theta_2$ is an unbiased estimator of $\mu$

b) $Var(\hat \theta_1) =\frac{1}{4} [\sigma^2 + \sigma^2 ] =\frac{\sigma^2}{2}$

$Var(\hat \theta_2) =\frac{1}{16} [\sigma^2 + 9\sigma^2 ] =\frac{5\sigma^2}{8}$

Step-by-step explanation:

For this case we know that we have two random variables:

$X_1 , X_2$ both with mean $\mu = \mu$ and variance $\sigma^2$

And we define the following estimators:

$\hat \theta_1 = \frac{X_1 + X_2}{2}$

$\hat \theta_2 = \frac{X_1 + 3X_2}{4}$

Part a

In order to see if both estimators are unbiased we need to proof if the expected value of the estimators are equal to the real value of the parameter:

$E(\hat \theta_i) = \mu , i = 1,2$

So let's find the expected values for each estimator:

$E(\hat \theta_1) = E(\frac{X_1 +X_2}{2})$

Using properties of expected value we have this:

$E(\hat \theta_1) =\frac{1}{2} [E(X_1) +E(X_2)]= \frac{1}{2} [\mu + \mu] = \mu$

So then we conclude that $\hat \theta_1$ is an unbiased estimator of $\mu$

For the second estimator we have:

$E(\hat \theta_2) = E(\frac{X_1 + 3X_2}{4})$

Using properties of expected value we have this:

$E(\hat \theta_2) =\frac{1}{4} [E(X_1) +3E(X_2)]= \frac{1}{4} [\mu + 3\mu] = \mu$

So then we conclude that $\hat \theta_2$ is an unbiased estimator of $\mu$

Part b

For the variance we need to remember this property: If a is a constant and X a random variable then:

$Var(aX) = a^2 Var(X)$

For the first estimator we have:

$Var(\hat \theta_1) = Var(\frac{X_1 +X_2}{2})$

$Var(\hat \theta_1) =\frac{1}{4} Var(X_1 +X_2)=\frac{1}{4} [Var(X_1) + Var(X_2) + 2 Cov (X_1 , X_2)]$

Since both random variables are independent we know that $Cov(X_1, X_2 ) = 0$ so then we have:

$Var(\hat \theta_1) =\frac{1}{4} [\sigma^2 + \sigma^2 ] =\frac{\sigma^2}{2}$

For the second estimator we have:

$Var(\hat \theta_2) = Var(\frac{X_1 +3X_2}{4})$

$Var(\hat \theta_2) =\frac{1}{16} Var(X_1 +3X_2)=\frac{1}{4} [Var(X_1) + Var(3X_2) + 2 Cov (X_1 , 3X_2)]$

Since both random variables are independent we know that $Cov(X_1, X_2 ) = 0$ so then we have:

$Var(\hat \theta_2) =\frac{1}{16} [\sigma^2 + 9\sigma^2 ] =\frac{5\sigma^2}{8}$

7 0

3 years ago

Answer this for points and brainilest (work must be included)

marin [14]

Answer:

Step-by-step explanation:

4b + 5 = 1 + 5b

4 = 1b

4 = b

4 0

2 years ago

Write in Slope-intercept Form an equation of the line that passes through the given points.

serious [3.7K]

Answer:

Step-by-step explanation:

Slope =(x2-x1/y2-y1)

=(3-7/2+3)

-4/5

slope =-4/5

3 0

2 years ago

Identify the phase shift of each function. Describe each phase shift use a phrase like 3 units to the left

melisa1 [442]

Answer:

It moves horizontally 1/2 units to the left

It moves vertically 2 units up

Step-by-step explanation:

∵ y = Acos(Bx - C) + D

∵ y = 2 - 3cos(2x + 1)

∴ The phrase of shift:

∵ The horizontally shift is -C/B = - 1/2 = -1/2

∴ It moves 1/2 units to the left

∵ The vertically shift is D

∴ It moves 2 units up

7 0

3 years ago

Each side of a square classroom is 8 meters long. The school wants to replace the carpet in the classroom with new carpet that c

son4ous [18]

Because a square has 4 sides, you would multiply the 8 meters by 4. That would mean that the entire room is 32 squared meters. Then multiply the 32 meters by the cost ($35.00). The total cost of the new carpet is $1,120

5 0

2 years ago