Questions tagged [self-study]

A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

A routine exercise designed to test one's knowledge; often, but not exclusively, from a textbook, course, or test used for a class or self-study.

The following guidelines are for those who are asking and those who would answer self-study questions.

They are rooted in two principles:

  • It is okay to ask about homework. Homework is included in this self-study tag. This site exists to help people learn and provide a standard repository for questions in statistics and machine learning, both simple and complex, and this includes helping students.

  • Providing an answer that doesn't help a student learn is not in the student's own best interest. Therefore you should choose to treat self-study questions differently than other questions in order to avoid substituting for the student.

Asking about self-study questions

  • Make a good faith attempt to solve the problem yourself first. Showing a genuine attempt will help keep your question active. This can be demonstrated by a detailed description of your failed or incomplete or incorrect attempt(s).

  • Ask about specific problems you have encountered in your initial efforts. If you can't do that yet, try some more of your own work first or searching for more general help.

  • Be honest about the source of the question. Do this by adding the self-study tag and mentioning whether it is for some class in the question text. Provide reference to the book or material whenever available.

  • Quote the homework question exactly. If you try to paraphrase it, you might fail to paraphrase it correctly.

  • Be aware of school policy (if relevant). If your school has a policy regarding outside help on homework, make sure you are aware of it before you ask for/receive help here. If there are specific restrictions (for example, you can receive help, but not full solutions), include them in the question so that those providing assistance can keep you out of trouble. In particular, pay attention to plagiarism policy and plagiarism software when writing your own answer in order to avoid disciplinary consequences.

  • Only use suggestions you understand. It definitely won't help you later (after school, in later assignments, on tests, etc.) and it could be, at best, very embarrassing if you are asked to explain what you turned in. You can also comment on your own questions and answers to your questions regardless of your reputation, so feel free to use comments to ask for additional clarification (after making an honest attempt at understanding). You may always ask further questions once you tried and failed to understand points in some answers.

Answering self-study questions

  • Try to provide explanations that will lead the asker in the correct direction. Genuine understanding is the real goal for students, but trying to provide that is seldom unappreciated for any question. Give references that may help with the lack of background of the OP.

  • It's usually better to provide an incomplete solution (or code sample) if you believe it would help the student, using your best judgment. You can use pseudo-code and general descriptions first. In the spirit of creating a resource, you may come back after a suitable amount of time and edit your response to include more details, if the question seems like such information will have lasting value.

  • Don't downvote others who answer coursework-related questions in good faith, even if they break these guidelines. It is a better idea to suggest editing the response in a comment.

  • Leave positive comments. A student may be in the process of learning something obvious or is developing the good habits you'd expect from an expert. Add a respectful comment or answer that points them towards best practices and better style but also point out missing background necessary to the understanding of the question and its solution.

  • Don't downvote a homework question that follows the guidelines and was asked in good faith. CV explicitly accepts homework questions that follow the guidelines. Consider making helpful suggestions for improving the question instead.

  • The self-study tag should only be added by the one asking the question. If there's any room for doubt at all, it's best to leave it as is. Instead, always add a comment first requesting that the asker clarify the situation.

(Adapted from an SO post by Joel Coehoorn as suggested in a meta discussion)

8136 questions
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Confidence intervals for empirical CDF

I have 100 data points from a random process. How would I go about placing a confidence interval around the estimate of $\Pr(X>x)$? The distribution function is unknown and positively skewed. My first inclination would be to use a bootstrap based…
6
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1 answer

Why the sample mean is not a good (sufficient) statistic?

Consider a simple example of $X_{i}$ be i.i.d uniform distribution on the interval $[\theta,\theta+1]$. By strong low of large numbers, I may conclude that $$\overline{X}\rightarrow_{P} \theta+\frac{1}{2} $$ However, it is not so clear what is the…
6
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1 answer

Show that $\mathbb{E}(X)$ is finite?

Given $X$ has density function $$f(x)= \frac{e^{x}}{(1+e^{x})^2},\quad -\infty
user30438
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1 answer

Confidence interval for the number of trials before you've observed each outcome in the sample space?

My friend collects stickers. There are 200 unique stickers to be sticked into the album. As the album gets fuller, it gets less and less likely that any newly obtained sticker is not already in the album. I assumed every sticker to be obtained…
miura
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5
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1 answer

Is it possible for a Bayes estimator to be independent of the sample?

I am trying to derive the Bayes estimator. Without getting into the nuts and bolts of the question, basically I have an indicator loss function of the form $$L(\delta , \theta) = \mathbb{1}\{A\}$$ For an event $A$. I found that $EL(\delta,\theta…
Xiaomi
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5
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1 answer

Variational Inference - factorized distributions and evidence lower bound

I am looking into C.Bishop's Pattern Recognition and Machine Learning chapter 10. In section 10.1.1 (p.465) he's proceeding through an analysis of the evidence lower bound which goes on like so: \begin{align} \mathcal{L}(q) & =…
AutomEng
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5
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2 answers

If $P(|X-19.1| \leq a) = 0.98$ then why is it necessarily $P(\frac{X-19.1}{17} \leq \frac{a}{17})= 0.99$?

Suppose we have $\mu = 19.1$ and $\sigma = 1.7$. I need to find $a \in \mathbb{R}$ such that: $P(|X-19.1|\leq a) = 0.98$ Now in the correction, it is given that: $$P(|X-19.1|\leq a) = 0.98 \iff P\left(\frac{-a}{1.7} \leq \frac{X - 19.1}{1.7} \leq…
5
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4 answers

Student looking to practice

I am simply wondering how non-professionals practice the statistical techniques they have learned. I am a student and want to implement some of the techniques I am learning but don't know how to approach consistently finding problems that are at my…
5
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3 answers

Bayes rule and base rate

My homework question: An inspector suspects that the food in the factory she is inspecting has been contaminated with a harmful chemical c. Such chemical contamination occurs in 5% of factories producing this food. The inspector has a test A for…
4
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2 answers

Expressing a sum as a compound Poisson Distribution

I am given two Poisson distributions, $X_1$ and $X_2$ with parameters $\lambda_1=1$ and $\lambda_2=2$ respectively. Also given that $Y = -3X_1$ + $2X_2$, how do I represent $Y$ as a compound Poisson distribution? I know that I have to use the…
4
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3 answers

Normal distribution probability

The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal distributions with stocks having a mean of 15% and a standard deviation of 20%, and bonds having a mean of…
4
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2 answers

Proper way to check convexity or concavity for a function

I am working with a function I would like to check if it is convex or concave. The function is the next: $$f(x_1,x_2)= \max\{x_1^6,e^{x_1+3x_2^2},3x_1^2-x_1x_2+x_2^4-\log(x_2+2)\}$$ With $x_2>-2$ I knowusing derivatives I can check for one function…
Duck
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4
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2 answers

How to compare two reviews, when one has more participants than the other

Hi I only did some basic stats at school but now I need to rank some data for a project, and I've run into this kind of scenario Game A: 1000 Reviews, 900 Positive and 100 Negative, so 90% positive. Game B: 20 Reviews, 20 Positive and 0 Negative, so…
zenoh
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4
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2 answers

MOOC or other online class for advanced stats?

Are there any MOOC or other (free/cheap) online classes for advanced statistics? I'm thinking upper-level undergrad or introductory graduate level. Things like time series models, factor analysis, MLE, Bayesian statistics, etc.
3
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2 answers

How to test if counts differ across temporal categories?

I have a homework question in which data is taken from three months of hospital admission data. It is then split into six 4-hour groups (0000–400, 0400–0800, etc.). The data are given with just the hour group and one column containing a number of…
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