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3 years ago

5. A carton of ice cream holds 5 cups of ice cream. One serving of ice cream is 1 cups.

Mathematics

1 answer:

Anna35 [415]3 years ago

4 0

Answer:

5 servings

Step-by-step explanation:

1 serving is 1 cup so 5 servings is 5 cups

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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

Need help!!!!! hurryyy

Svetach [21]

hey ur ans is correct

28 is correct ans

tysm for question

8 0

3 years ago

Read 2 more answers

In the 1996 presidential election, Bill Clinton received 2,495,683 votes in Texas. This was 177,868 more votes than he had recei

lilavasa [31]

Answer:

Votes did Bill Clinton get in Texas in 1992 = 2317815

Step-by-step explanation:

Total votes received by Bill Clinton in 1996 = 2,495,683

Given that this was 177,868 more votes than he had received in 1992.

So the vote received in 1992 by Bill Clinton in 1992 is = ( Total votes received by Bill Clinton in 1996 ) - ( 177,868 )

⇒The vote received in 1992 by Bill Clinton in 1992 is = 2,495,683 - 177,868

⇒The vote received in 1992 by Bill Clinton in 1992 is = 2317815

Therefore votes did Bill Clinton get in Texas in 1992 = 2317815

5 0

3 years ago

A. < DCA<br> b. < BCA<br> c. < BAC <br> d. < CAE

Brrunno [24]

I would say the answer is C. It has been a while since I’ve taken geometry but I am pretty sure the angle would be the middle letter.

5 0

3 years ago

What is the grade if there are 85 questions and u miss 9

Irina18 [472]

If you miss 9 questions, the how many did you get right?

85 - 9 = 76

So now you got 76 out of 85 correct or 76/85...

Now if you just do the fractional division that is described by the fraction you will get the answer. The fraction bar literally means "divided by", so the fraction means...

76 divided by 85 which equals...

.8941

Now to convert to percentage we multiply by 100 (move the decimal 2 places to the right)

.8941 x 100 = 89.41% Round to nearest one percent...

89%

5 0

3 years ago