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2 years ago

Help me on this math question

Mathematics

1 answer:

deff fn [24]2 years ago

6 0

Answer:

9. $0$

10. $\frac{1}{2}\\$

Exaplanation:

<em>Please refer to my Answer from this question to know more about the slope of a line: <u>brainly.com/question/24599351</u></em>

In graph 9, we can see a line that is perfectly horizontal. Graphs of lines that are horizontal has a slope of, $0$ .

If you want we can still solve for the slope of the line in graph 9, without acknowledging that the line is horizontal.

In graph 9, we can see that the points, $(-4,-1)$ and $(2,-1)$ , is on the line. These can be our points $1$ and $2$ .

$m = \frac{-1 -(-1)}{2 -(-4)} \\ m = \frac{-1 +1}{2 +4} \\ m = \frac{0}{6} \\ m = 0$

In graph 10, we can see that the points, $(0,-2)$ and $(2,-1)$ , is on the line. These can be our points $1$ and $2$ .

$m = \frac{-1 -(-2)}{2 -0} \\ m = \frac{-1 +2}{2 -0} \\ m = \frac{1}{2} \\$

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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:

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

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3 years ago

15 less than a number S is three more than 9 times a number T. Solve for S

lbvjy [14]

Answer:

s = 9t + 18

Explanation:

Set up your equation

s - 15 = 9t + 3

Now get s by itself by adding 15 to both sides

s + 0 = 9t + 3 + 15

s = 9t + 18

If you know the value of t, plug that into the equation to solve further.

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What is the image point of (3,9) after a translation right 3 units and up 1 unit.

bezimeni [28]

Answer:

4,6

Step-by-step explanation:

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The wholesale price of a sweater is $35. The retail price of the sweater is 10% more than the wholesale price. What is the retai

PilotLPTM [1.2K]

Answer:

$38.50

Step-by-step explanation:

35/10 =3.5

35+3.5=38.5=$38.50

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3 years ago