WhatsApp us

# Estimation

Need a hand with your homework? Get expert help now and smash those grades! 💯 Submit your assignment today!

100% human expertise, no AI. 🤖

• Experienced Tutors
• On-Time Delivery
• Plagiarism-Free Work
Order Homework Help From Experts
What should we call you?
Zero spam guarantee.

The process of drawing a sample from a population and to gather information about the parameter through a reasonably close function is known as estimation. This is done in order to find out the unknown parameters which we encounter in a population and which hinders our estimation and conclusion about a population. Thus this process is used to find out the parameters. The value obtained from such a process is known as estimated value and the function is called estimator.

An estimator is supposed to possess the qualities stated below to perform well. They are:

1. Un biasedness

A statistic t is an unbiased estimator of a parameter , if E[t] =

If not, then the estimator is biased.

There are quite a few theorems stated below which proves this.

Theorem 1:

Prove that the sample mean x is an unbiased estimator of the population mean µ

Proof:

Let x₁, x₂, …, , be a simple random sample with replacement from a finite population of size N, say, X₁, X₂,… ,

µ=

Prove E(x) =µ

While drawing xi, it can be one of the population members i.e., the probability distribution of Xi can be taken as follows:

 X₁ X₂ … probability 1/N 1/N 1/N

Therefore,

E (  = X₁*  + X₂*  +….+ *

=

= µ, i= 1, 2,…., n

E (  = E [( ]

= [E (

If the population is finite or the sampling is done without replacement, the same result will be obtained.

Theorem 2:

The sample variance S²=  is a biased estimator of variance σ².

Proof:

Let x₁, x₂, …,  be a random sample from an infinite population with mean σ and variance σ².

Then, E (x) = µ, Variance (xi) = E (xi – µ)² = σ², where i= 1, 2, … ,n.

S²=

=

=  where  xi – µ and standard deviation is unaffected by change in origin.

= – µ)²

E (s²) = – µ)²

= )= σ²-

Thus, s² is a biased estimator of σ².

Also, Let S²=

E (s²) =

= σ²

= σ²

Therefore, s² is a biased estimator of σ².

Example: A population consists of 4 values 3, 7, 11, 15. Draw all possible sample of size two with replacement. Verify that the sample mean is an unbiased estimator of the population mean.

Solution:

No. of samples = 42 = 16, which are as below:

(3, 3), (7, 3), (11, 3), (15, 3)

(11 , 7), (15, 7), (11 , 11), (15, 11)

(11, 15), (15, 15), (3, 7), (7, 7),

(3, 11), (7, 11), (3, 15), (7, 15)

Population mean µ= = = 9

Sampling distribution of mean

 Sample mean Frequency f .f 3 1 3 5 2 10 7 3 21 9 4 36 11 3 33 13 2 26 15 1 15 Total 16 144

Mean of sample = = 9

Since E ()= µ

Therefore, sample mean is an unbiased estimator of population mean.

1. Consistency

A statistic  obtained from a random sample of size n is said to be a consistent estimator of a parameter if it converges in probability to θ as n tends to infinity.

Alternatively, If E [ ] θ and Var [ ] 0 as n ∞, then the statistic  is said to be consistent estimator of θ.

Example:

When sampling from a population N,

E )= µ and )= → 0 as n→

Therefore, sample mean is a consistent estimator of population mean.

1. Efficiency

A parameter might comprise of more than one consistent estimator. Let T1 and T2 be two consistent estimators of a parameter θ. If Var (T₁) < Var (T₂) for all n, then T₁ is said to be more efficient than T₂ for all size.

1. Sufficiency

Let x₁, x ₂, … , be a random sample from a population whose pmfor pdfisf (x, 8). Then T is said to be a sufficient estimator of e if  f (x₁, ). f(x₂, )…..f( , ) = g1(T , ). g₂( x1,x2,…,

Where g1(T , ) is the sampling distribution and g₂( x1,x2,…,  is independent of .

Even though sufficient estimators exists only in certain cases, but when random sampling for a normal population, the sampling mean x is a sufficient estimator of µ.

Pricing may change based on requirements

l

## FAQ - Our Homework Help Services

We have put together some commonly asked questions.

K
L

### Is there a website that can do my homework?

Yes, if you are looking for such a site, MyHomeworkHelp is one of the leading homework help websites that can do your homework and assist with various academic needs. Here's all you need to know about our team and how they provide flawless homework help.

If you find yourself thinking, "I need to pay someone to do my homework," our team is ready to assist. It's common for students to seek help with their homework, and our experts are prepared to provide personalized support tailored to your needs.

You can visit www.myhomeworkhelp.com to get all types of homework-related help from our experts.

K
L

### What is the best homework help website?

The best homework help website enhances students' experience of getting homework assistance from experts. MyHomeworkHelp, recognized as one of the best online homework help platforms, serves as both a guide and a solution provider for students. We've been rocking the homework help scene since 2012, assisting over 20k students, and we must be doing something right because more than 70% of them keep coming back for more. Whether you need help understanding concepts, completing assignments, or getting your homework done, MyHomeworkHelp is here to support your academic journey as the best college homework website.

K
L

### How can I get help with my homework?

1. Tell us your homework details

To get started with online homework help, simply choose the type of homework assistance you need. When filling out the order form, make sure to provide detailed instructions, including the deadline, number of pages, grading rubric, and any other relevant information.

Review the details of your homework order and proceed to make a secure payment using VISA, Mastercard, or PayPal. Once the payment is processed, our experts will begin working on your homework immediately.

The completed homework will be delivered directly to your email. This ensures that students receive their homework assistance on time and can meet their academic requirements without stress.

K
L

### Do you guarantee plagiarism-free homework answers?

We take academic integrity very seriously and understand the importance of providing homework answers free of plagiarism. Our tutors are committed to delivering original and unique content for every assignment. Here are the steps we take to ensure your homework is plagiarism-free:

1. Original Work: Each assignment is completed from scratch based on your specific requirements and guidelines.
2. Expert Tutors: Our tutors are highly qualified and experienced in their respective fields, ensuring the work they produce is both original and high-quality.
3. Plagiarism Detection: We use advanced plagiarism detection software to scan every assignment before delivery. This ensures that the content is unique and free of any copied material.
4. No AI Usage: We guarantee that all work is 100% human-crafted expertise, with no AI-generated content involved. This ensures the authenticity and quality of the work provided.
5. Quality Assurance: Our quality assurance team reviews each assignment for originality and adherence to academic standards before it is sent to you.

By following these stringent measures, we guarantee that the homework answers you receive are completely free of plagiarism and AI involvement. You can trust us to provide you with original and high-quality academic assistance.

K
L

### Is your homework service confidential?

Absolutely! Confidentiality is one of the basic guarantees of our service at MyHomeworkHelp.com.

When our customers make their homework orders, they know their information remains 100% confidential.

Even your homework writer will not be provided with your personal details. So, when you hire a professional homework helper on our website, rest assured that your information will remain private and safe.

K
L

### How much do I need to pay to get my homework done?

We do not have monthly fees or minimum payments for our services. Each homework assignment is quoted a unique price, based on the tutor’s estimate of the time required to complete your work. There are no obligations, and you are free to discuss the price quote with the tutor.

When you decide to pay someone to do my homework, our pricing starts at \$13.99 per page. The final pricing depends on various factors including the page count, deadline, nature of the task, and the homework writer’s level of expertise.

We offer flexible payment options, allowing you to make a partial payment to start working on your assignment and pay the remaining amount upon completion. This ensures no pressure of up-front payment and no hidden order costs.

Our dynamic pricing model takes into account the type of assignment, its urgency, and the complexity of the task. For instance, shorter deadlines and more complex assignments may increase the price. You can get an instant quote by selecting your assignment type, deadline, and page count on our website.

K
L

### Who are the experts who will help me with my homework?

We work with subject experts from all over the world. We hire them with the help of complex tests in the disciplines of their expertise. We also verify the IDs and academic transcripts of our homework writers to be sure that our experts have a bachelor's or master’s or a PhD degree. This is how we can be sure of the proficiency of our panel of experts who will help you with your homework. Here's all you need to know about our team and how they provide flawless homework help.

1. Our team comprises top-tier homework helpers who excel in addressing and resolving questions on various topics. Each tutor effectively utilizes their expertise to concentrate on the core subject matter and thoroughly analyze it.
2. Our professional tutors specifically craft each assignment tailored to students' requirements, including preferred formats, citation styles, and essential elements.
3. Whether it’s coursework, dissertations, essays, or case studies, our platform guarantees timely college homework help across a wide range of academic papers. Don’t hesitate any longer; connect with our tutors when you seek help with your homework for perfect assignment solutions and improved grades.

K
L

### Can I chat with my homework helper for updates?

Yes, you can certainly chat with your homework helper on our secure chatboard platform. MyHomeworkHelp.com provides a direct communication channel between you and your assigned expert (while maintaining privacy). This feature allows you to ask questions, clarify instructions, and provide additional information about your homework order to ensure that the help you receive is tailored to your specific needs.

You'll be notified by email whenever there are new messages for you, but we advise regularly checking your personal page to ensure no critical updates from your writer are overlooked.

Should you have an urgent matter to address, do not hesitate to contact the support team for assistance. This system ensures that students can stay updated on their homework paper progress and maintain clear communication with their experts.

K
L

### What makes you the best homework helper?

MyHomeworkHelp is ranked as one of the best online homework helpers, providing exceptional support to students. We've been excelling in the homework assistance arena since 2012, assisting over 200k students, and consistently achieving high satisfaction rates, with more than 70% of our students returning for additional help. But do not take our word for it! See our independent reviews on google, facebook, sitejabber, and on Trustpilot. For all collated reviews, see here

We ensure our prices remain competitive and offer attractive discounts to make our services accessible. Our commitment to delivering plagiarism-free solutions guarantees the integrity and originality of your assignments. These attributes, combined with our dedication to personalized support and timely delivery, establish MyHomeworkHelp as the premier homework helper for all your academic needs.

K
L

### How will I receive my homework order?

You'll receive the initial version of your paper as a secure, non-editable PDF within your specified deadline. This allows you to review the content and decide if any revisions or edits are required. Our homework service will refine the homework paper based on your feedback.

Should the document meet your expectations and not require any changes, you can simply approve the order and access the editable Word .doc file.