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3 years ago

Make a general rule about scale factor, perimeter ratio, and area ratio.

Mathematics

1 answer:

evablogger [386]3 years ago

5 0

Answer: A Scale factor is a number which multiplies or scales a number in an equation.

Perimeter ratio is the ratio of the perimeter to the area.

Area ratio is the ratio of the total amount of usable floor a land has

Step-by-step explanation:

Scale ratio can be established by this simple equation y=CX where C is the scale factor.

Perimeter ratio; perimeter = 2(L+B) where L is length and B is breadth

Area = L×B

Therefore perimeter ratio = 2(L+B)/L×B

Area ratio; L2 ×W2/L1×W1 where L1 and L2 are the lengths and W1 and W2 are the widths.

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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

Find the slope of the line passing through the points (7, -2) and (3, - 7).

professor190 [17]

Answer:

m = $\frac{5}{4}$

Step-by-step explanation:

To find the slope, we have to use the slope formula:

m = $\frac{y_2 -y_1}{x_2 - x_1}$ .

Let $(x_1,y_1) = (7, -2)$ and $(x_2,y_2) = (3, -7)$ . Then

m = $\frac{(-7)-(-2)}{3-7} = \frac{-5}{-4} = \frac{5}{4}$

3 0

3 years ago

Find the value of each variable in the following parallelograms.

Stella [2.4K]

Answer:

x = 15

y = 7.5

Step-by-step explanation:

✔️Diagonals of a parallelogram bisect each other at 90°.

Therefore,

2x° + 60° + 90° = 180° (sum of triangle)

Solve for x

2x + 150 = 180

2x = 180 - 150

2x = 30

2x/2 = 30/2

x = 15

✔️2x = 4y (alternate angles/corresponding angles)

Plug in the value of x

2(15) = 4y

30 = 4y

30/4 = y

7.5 = y

y = 7.5

7 0

3 years ago

which measurment represents the height of the parallelogram? please answer asap i need this done soon! thabk you so much!

iVinArrow [24]

3 meters represents the heigh of the parallelogram. It's just the length of a straight line from the base to the top.

3 0

3 years ago

Choose Yes or No to tell whether each rate is a unit rate. 1/1/3 Choose... 2/3/1 Choose... 2/3 Choose... 3/1 Choose...

MariettaO [177]

Answer: No and yes and no and yes??? ;-;

Step-by-step explanation:

5 0

3 years ago

Make a general rule about scale factor, perimeter ratio, and area ratio.​

Make a general rule about scale factor, perimeter ratio, and area ratio.