in how many ways can the letters in the word 'population' be arranged?

The MLE of σ² is a biased estimator of σ²

The maximum likelihood estimator (MLE) of σ² is a biased estimator, we need to demonstrate that its expected value is different from the true population variance, σ².

Let's start with the definition of the MLE of σ². In the context of simple linear regression, the MLE of σ² is given by:

MLE(σ²) = SSE/n

where SSE represents the sum of squared errors and n is the number of observations.

The expected value of the MLE, we need to take the average of all possible values of MLE(σ²) over different samples.

E(MLE(σ²)) = E(SSE/n)

Since the expectation operator is linear, we can rewrite this as:

E(MLE(σ²)) = 1/n × E(SSE)

Now, let's consider the expected value of the sum of squared errors, E(SSE). In simple linear regression, it can be shown that:

E(SSE) = (n - k)σ²

where k is the number of predictors (including the intercept) in the regression model.

Substituting this result back into the expression for E(MLE(σ^2)), we get:

E(MLE(σ²)) = 1/n × E(SSE)

= 1/n × (n - k)σ²

= (n - k)/n × σ²

Since (n - k) is less than n, we can see that E(MLE(σ²)) is biased and different from the true population variance, σ².

Therefore, we have shown that the MLE of σ² is a biased estimator of σ².

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The question is incomplete the complete question is :

Show that σ² = SSE/n, the maximum likelihood estimator of σ² is a biased estimator of σ²?

Answer:

6.25

Step-by-step explanation:

Divide 150 $ to 24 caps on your calculator

If the cost of 24 caps is $150, then the cost of each cap is $6.25.

We know that a single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method. We typically use this technique for math calculations. We are able to locate the missing value using the unitary method.

Given that the cost of 24 caps is $150.

Then the cost of 1 cap is 150/24 = $6.25

Therefore we can conclude that If the cost of 24 caps is $150, then the cost of each cap is $6.25.

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Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

Answer:

\(81124\ miles\)

Step-by-step explanation:

\(We\ are\ given,\\No.\ of\ miles\ a\ satelite\ flies\ in\ 7.36\ hours=50048\ miles\\To\ find:\\The\ no.\ of\ miles\ it\ has\ flown\ in\ 11.93\\Now,\\We\ can\ solve\ this\ by\ constructing\ a\ proportion,\\A\ proportion\ is\ simply\ represented\ in\ this\ format:\\\frac{x_1}{y_1}=\frac{x_2}{y_2}\\Here,\\x\ represents\ Miles\ while\ y\ represents\ Hours.\\Hence,\\x_1=50048\ miles\\y_1=7.36\ Hours\\x_2=x_2\\y_2=11.93\ Hours\\Hence,\ by\ setting\ up\ a\ proportion\ we\ get,\\\)

\(\frac{50048}{7.36}=\frac{x_2}{11.93}\\Now,\ by\ solving\ the\ equation,\\6800*11.93=x_2\\x_2=81124\ miles\)

Answer:

14

Step-by-step explanation:

Ok, 60! is a really big number

\(x!=x(x-1)(x-2)...1\)

So we have 60*59*58...*1

2 times 5 is 10 which makes a terminal zero (ending zero)

We need to count how many fives and twos are in 60!

There are 60/5=12 5^1's

There are 60/25=2 5^2's

So 12+2=14

There are way more 2's than fives so we take the lesser number

So the answer is 14

*Note that 60/25 is not 2, we need an integer rounded down

Answer:

2) x=11

Step-by-step explanation:

1) u got the first one right x=90°

2)

2x-1+69=90

2x-1=21

2x=22

x=11

(a). There is a 5.26% chance that the metal ball falls into a green slot.

(b). There is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

(c). P(00 or red)  ≈ 0.5263

(d). This event is called impossible.

(a) P(green) = 2/38 = 1/19 ≈ 0.0526.

This means that there is a 5.26% chance that the metal ball falls into a green slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 5 spins to end with the ball in a green slot. (Expected value = 100 x P(green) = 100/19 ≈ 5.26, which we round to the nearest integer.)

(b) P(green or red) = P(green) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 53 spins to end with the ball in either a green or red slot. (Expected value = 100 * P(green or red) = 2000/38 ≈ 52.63, which we round to the nearest integer.)

(c) P(00 or red) = P(00) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either 00 or a red slot on any given spin of the roulette wheel.

(d) The probability that the metal ball falls into the number 31 and a black slot simultaneously is zero, since 31 is an odd number and all odd numbers are red on the roulette wheel. This event is called impossible.

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Answer:

Let's assume that the distance between Chicago and Hoopertown is represented by 'x' miles.

According to the given information:

Raymond lives 23 miles from Chicago, so the distance between Amanda and Chicago is 23 - 15 = 8 miles.

Since Amanda lives halfway between Charlie and Chicago, the distance between Charlie and Chicago is also 8 miles.

Therefore, the distance between Charlie and Hoopertown is x - 8 miles.

Since Charlie lives halfway between Chicago and Hoopertown, the distance between Raymond and Charlie is (x - 8) / 2 miles.

Given that Raymond lives 15 miles from Amanda, we can set up the following equation:

(x - 8) / 2 = 15

To solve for x, we can multiply both sides of the equation by 2:

x - 8 = 30

Next, we can isolate x by adding 8 to both sides of the equation:

x = 38

The interval that corresponds to the smallest area under a Normal curve is option D, μ - σ to Q3. This is because it covers only one standard deviation below the mean (μ - σ) and a smaller portion of the upper tail (up to Q3) compared to the other options. Smaller intervals generally correspond to smaller areas under the curve.

The interval that corresponds to the smallest area under a Normal curve is option D, μ - σ to Q3. This is because it covers only one standard deviation below the mean (μ - σ) and a smaller portion of the upper tail (up to Q3) compared to the other options. Smaller intervals generally correspond to smaller areas under the curve. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable whose distribution converges to a normal distribution as the number of samples increases. Therefore, physical quantities that are expected to be the sum of many independent processes, such as measurement errors, often have distributions that are nearly normal.

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Answer:

f '(x) =6x² +2x-8+5by

Step-by-step explanation:

The figure H''B''G''P'' created following the transformations applied to HBGP such that HBGP is larger than  H''B''G''P'', inverted and on the other side of the y-axis indicates;

The completed table is presented as follows;

\(\begin{array}{|c|c|c|c|c|\pi \pi }\text{Preimage} &\text{Side Length} & \text{Image} &\text{Side Length}&\text{Ratio of Preimage to Image Lengths } \\GB & 5 &G''P'' &2.5&2:1 \\PH &3 & P''H'' &1.5&2:1 \\HB & 5 & H''B'' &2.5&2:1 \\BG &3 & B''G'' & 1.5& 2:1 \\\end{vmatrix}\)

A geometric transformation involves making changes to a geometric figure.

The coordinates if the vertices of the quadrilateral HBGP are;

H(-1, -2), B(-6, -2), G(-6, 1), and P(-1, 1)

The approximate coordinates of the vertices of the quadrilateral H''B''G''P'' are;

H''(0.5, 1), B''(3, 1), G''(3, -0.5), P''(0.5, -0.5)

The length of the side GP in quadrilateral HBGP = -1 - (-6_) = -1 + 6 = 5

Length of the side PH in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

Length of the side HB in quadrilateral HBGP = -1 - (-6) = -1 + 6 = 5

Length of the side BG in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

The possible transformations applied to HBGP to create H''B''G''P'' includes;

A dilation, a rotation of 180° and a translation

The length of the side G''P'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side P''H'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

The length of the side H''B'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side B''G'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

Ratio of the side length of GP to the side length of G''P'' = 5:2.5 = 2:1

Ratio of the side length of PH to the side length of P''H'' = 3:1.5 = 2:1

Ratio of the side length of HB to the side length of H''B'' = 5:2.5 = 2:1

Ratio of the side length of BG to the side length of B''G'' = 3:1.5 = 2:1

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Answer:

true

Step-by-step explanation:

I'm pretty sure it's trur

¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿???????????????

Very sry to tell that I really don't know it...

The value of the 'x' is 3.7 units

Given a right-angle triangle, Hypotenuse is 15 units and one of the angles is 42°

To find 'x' We have to use trigonometric ratios

The cosine (cos) of an angle in a right triangle is the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

cos θ = Adjacent Side / Hypotenuse.  

From the figure, The length of the Adjacent side of the angle = x and the length of Hypotenuse = 15

cos 42° = x/15

0.74 = x/5

Multiply by 5 on both sides

5 [x/5] = 5 × 0.74

x = 3.7

Therefore, The value of the 'x' is 3.7 units

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Answer: 80

Step-by-step explanation: The question is tell us that a certain company  we don't know which one, but it says a certain company has 400 shoes. that is important to note. also 20% of the shoes are black. and One shoe is chosen and replaced. Then the second shoe is chosen. The question is What is the probability that the shoes chosen are black?

Well, take 400 and mutipy it by 20% which changes to 0.20 in decimal form then mutiply your answer by one and you get 80. so the answer is the probability that shoes chosen are black is 80%.

Step-by-step explanation:

  Radical already isolated

    √163 = x

Raise both sides to the second power

    (√163)2 = (x)2

    After squaring

    163 = x2  Rearranged equation

    x2  -163 = 0

    This equation has two real roots:

      x1 = ( 0 + sqrt(652) ) / 2 = 12.7671

     x2 = ( 0 - sqrt(652) ) / 2 = -12.7671  Original equation

    √163 = x

    Plug in 12.7671 for  x  

     √163 = (12.7671)

     Simplify

     √163 = 12.767

     Solution checks !!

    Solution is:

     x = 12.7671   Original equation

    √163 = x

    Plug in -12.7671 for  x  

     √163 = (-12.7671)

     Simplify

     √163 = -12.767

     Solution does not check

     12.767 ≠ -12.767

Answer:

I AINT SOLVING ALL THAT

Answer:

\(170in^3\)

Step-by-step explanation:

\(V=\pi r^2h=\pi *3^2*6=169.646\\=170in^3\)

The experiment compared the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type. For 32 high-purity specimens, the sample average toughness was X=65.5, while for 38 commercial-purity specimens, the sample average toughness was y=59.8.

The high-purity steel is more expensive, and its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Both toughness distributions are assumed to be normal with σ1 = 1.2 and σ2 =1.1. Using α=.001, the relevant hypotheses are tested. β is then computed for the test when μ1 – μ2 = 6.
In the experiment, the fracture toughness of high-purity 18 Ni maraging steel (X = 65.5, m = 32, σ1 = 1.2) was compared to commercial-purity steel (Y = 59.8, n = 38, σ2 = 1.1). The goal is to justify the use of high-purity steel if its toughness exceeds commercial steel by more than 5. Both toughness distributions are assumed to be normal.

a. To test the relevant hypotheses using α = .001, we perform a two-sample t-test. The null hypothesis (H0) is that the difference in means (μ1 - μ2) is less than or equal to 5, and the alternative hypothesis (H1) is that the difference is greater than 5.

b. To compute β for the test conducted in part (a) when μ1 - μ2 = 6, we need to determine the probability of a Type II error, which is the likelihood of failing to reject the null hypothesis when it is false. Calculating β requires knowledge of the sampling distributions and the specific alternative value (μ1 - μ2 = 6).

In summary, to justify the use of high-purity steel, a two-sample t-test can be conducted using the given parameters. Additionally, calculating β helps understand the likelihood of a Type II error in this hypothesis test.

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The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°

Sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:

a/sinA = b/sinB = c/sinC

Where A,B,C are the angles and a,b and c are the opposite sides to the angles.

1)

A = 55°, a = 10. 1, b = 12. 3

10 / sin(55) = 12.3 / sinB

B = 86.01°

A + B + C = 180° (angle in triangle)

55 + C + 86 = 180

C = 39

10 / sin(55) = c / sin(39)

c = 7.68

The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°

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Answer:

Step-by-step explanation:

80*60%= 48 free throws were made

Answer: 48

Step-by-step explanation:

80x 0.01=0.8

0.8x 60=48

Step-by-step explanation:

s.i=prt

=500×0.03×3

=45

The type of sampling in the scenario given is a random sampling. There are different types of sampling techniques, which include simple random sampling, stratified sampling, systematic sampling, cluster sampling, etc.

Random sampling is a type of sampling technique in which every member of the population has an equal chance of getting selected in the sample.

This sampling method is unbiased and a representative of the population.

It is important to use this sampling technique when we have a large population with a wide range of characteristics.

In this scenario,

the students are randomly selected from the bag, and each student is given a number from 1-125, and their numbers are written on a small piece of paper and put in a large bag mixed thoroughly, and then 12 numbers are randomly selected from the bag.

Hence, we can say that the type of sampling in the given scenario is a random sampling.

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Answer:

I believe it would be -3,4.

Step-by-step explanation:

To find slope you use rise over run, where you count up first, then go to the side. If you count down on the left you count 3 boxes, but since its going down its negative. And to get the run you count over 4. Meaning it's -3,4

There is a probability of around 60% that during a week picked randomly, the combined sum of their earnings will be below $0.2533.

The given probability is a measure of the chances that the occurrence of an event will happen. In the context of the question, we want to calculate the combined total of earnings that are less than a certain amount. We know that the probability is approximately 0.6. Therefore, the answer is given by the value that satisfies this condition.

That is, P(X < a) = 0.6where X represents the combined total earnings of a randomly selected week, and a is the required amount.

To solve for a, we can use the cumulative distribution function (CDF) of X. The CDF gives the probability that X is less than or equal to a. Therefore, CDF(a) = P(X ≤ a)

The complement of this probability isP(X > a) = 1 - CDF(a)

We know that P(X < a) = 0.6, which is equivalent to (X ≤ a) = P(X < a) + P(X = a) = 0.6 + 0 = 0.6

Therefore, P(X > a) = 1 - CDF(a) = 1 - P(X ≤ a) = 1 - 0.6 = 0.4

Now we can use a calculator to find the value of a that corresponds to P(X > a) = 0.4.

For example, if we use a calculator, we get a value of a = 0.2533 (rounded to four decimal places).

Therefore, the probability is approximately 0.6 that in a randomly selected week, they will make a combined total of less than $0.2533.


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Answer:

1. is D

2. is A

Step-by-step explanation:

The Titanic could stay afloat with four of its 16 watertight compartments flooded, more than anyone could imagine on a ship of its size. ... As the ice bumped along its starboard side, it punched holes in the ship's steel plates, flooding six compartments. In a little over two hours, the Titanic filled with water and sank.