# 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.

7,701 questions
Filter by
Sorted by
Tagged with
59 views

### Looking for a predictive prior for what I thought to be Bayesian Analysis

I need a prior with 2 parameters location (μ) and scale (σ) (a transformation of mean and standard deviation). My distribution is over discrete values, equally spaced with distance $c$ between ...
27 views

27 views

### Validating Randomization

Was the randomization successful in the table below? Why or why not? and How does one get to know this?
46 views

### Statistical inference question evaluating a joint probability mesure w.r.t. a distribution

Note: I have edited this question and delted my old question after following the guidlines to be more clear. I hope this new question is clear and well posed. I attempted this question but I got stuck ...
1 vote
32 views

### Prove sample minimum and unbiased sample variance are independent

I have a simple random sampling (n observations) of the population $X$, whose pdf is $$f_\theta (x) = e^{-(x-\theta)} I_{(\theta,\infty)}(x)$$ and $\theta \in \mathbb{R}$. $S^2_n$ is the unbiased ...
45 views

### What does capital D above an equal sign mean?

I was beginning to self study time series and came across this notation: $\stackrel{\mathcal{D}}{=}$. I wonder what it means? (I have limited access to the textbooks for the moment, so I have to post ...
1 vote
56 views

### Hypothesis testing for $\sigma^2$ in linear regression

I'm trying to figure out a way to test hypotheses about variance in the linear regression model. The hypotheses I want to test are: \begin{align*} &H_0:\sigma^2=1\\ &H_1:\sigma^2<1 \end{...
1 vote
37 views

### Expectation of the product of multiple correlated 1-D normal variables [duplicate]

First question: is it possible to have a set of $k$ random variables $\left\{X_i\right\}$ s.t. each $X_i \sim N(0,1)$ individually, and $\text{Corr}(X_i,X_j)=\rho$, $∀i\neq j$? If those conditions are ...
1 vote
29 views

27 views

### Assessing the effectiveness of a teaching tool by paired t-test

You have been asked to assess the effectiveness of a new teaching tool. A sample of 25 students from your classes have been tested before and after the provision of the tool, so each student has two ...
31 views

### power and sample size estimation

For a one-sided test: $$H_0: \mu_1 \leq \mu_2 \ H_1: \mu_1 >\mu2$$ $$\alpha=0.025,\beta=0.1$$ How to calculate the sample size needed? Is this information enough to calculate the sample size?
1 vote
22 views

### No previous information in a clinical trial [closed]

I'm conducting a clinical trial with a treatment group and a placebo group and calculated the sample size based on a previous study. However, I would like to add two more new placebo groups with ...
183 views

### Finding the MVUE of the center of a circle of unknown location

Is there a known analytic solution for finding the minimum variance unbiased estimator of a disk of an unknown location given that a sample of $n$ points was drawn uniformly and randomly from the disk ...
1 vote
27 views

### Finding the non-zero region of a marginal

Basic question but: what happens to the region on which a pdf is non-zero when a bivariate is integrated to get a marginal? The example I'm working on (course problem booklet for a mathematics BSc ...
41 views

### Calculate sample size for clinical trial without raw data

Usually, we calculate the sample size needed for a clinical trial based on a former clinical trial which shows there is a significant effect. What if there is no such a trial? What if there is no ...
104 views

From One Thousand Exercises in Probability I found the exercise: Galton's paradox. You flip three fair coins. At least two are alike, and it is an even chance that the third is a head or a tail. ...
24 views

### $E(SN)$ for aggregate claim amount $S$, $S=X_{1}+...+X_{n}, X_{i}$ are iid [duplicate]

Consider the following model for aggregate claim amounts $S$: $S=X_{1}+X_{2}+...+X_{N}$ where the $X_{i}$ are independent, identically distributed random variables representing individual claim ...
1 vote
36 views

### When does a difference in means not capture the true treatment effects vs a regression with pre-treatment controls?

A question from Gelman - Regression & Other Stories... In answer to my own question...my understanding is that a difference in means should not capture the treatment effect when there are pre-...
21 views

### Bayesian model comparison with systematic error

Two parameters $(x,y)$ were measured for 3 different objects, wielding the following results: $$\{ (x,y) \}= \{ (1,3), (3,5), (5,9) \}$$ Knowing that the error in the estimation of the values $y$ is ...
38 views

### question of a Poisson random effect model

Assume a Poisson random effect model (with a random intercept) $$\log E(Y_{it}|b_i,x_i)=\beta_0+\beta_1x_i+b_i$$ $$b_i \sim N(0,\tau^2)$$ How to derive the population-averaged effect of one unit ...
52 views

### football probability

I have the following problem: Suppose that the probability of a football team (T) to win the match with 2-1 is p1 and, given that T scores a goal, the probability that the best player of the team ...
14 views

### find a suitable statistical method to analyze Yes/ No type qualitative data

I have done a survey on finding the applicability of Co- management system on a reservoir. This survey contains 8 main points. Under one main point, I included some Yes/No questions (No of questions ...
1 vote
36 views

### Why does my ARIMA predictions on monthly data form a straight line?

For short detail, the goal was to forecast using 51 monthly observations of KPI of project implementations which I aggregated by sum from 463 observations from about 4 years of data (May 2017 to July ...
32 views

### Confidence interval for the parameter of a random variable

I am studying statistics, and I came across a problem that I am not sure if what I am doing is correct or if there is some other way to do this. Any feedback is appreciated. I divided in 2 problems, ...
23 views

### How to add change (in unemployment rate) to dependent variable

I'm an Econometrics beginner and I'm sorry if the title is confusing. I basically have a variable “unemp” which gives me the unemployment, the dependent variable of this model should be the change in ...
31 views

### Tail-equivalence implying same domain of attraction

Suppose two distributions F and G that have the same extreme point ($x^F = x^G$) and $$\lim_{x \to x^F}\frac{\bar{F}(x)}{\bar{G}(x)} = c \in (0, \infty)$$ Show that F and G belongs to the same domain ...
26 views

### How to test for significance with t-test and interaction variables? [duplicate]

I need to answer this question for my Econometrics class: "Does the gender gap differ significantly in urban versus non-urban areas? Test at the 5% level". I think I need to use the t-test ...
24 views

### Standardization in Machine Learning Models

Please answer this question in two contexts: Context 1 - Performance: Which models are sensitive AND which models are insensitive to standardization? Why? Are there any edge-cases in which ...
26 views

### What's wrong with this conditional probability working?

A past exam paper for my course (BSc Mathematics, second-year module in statistical inference and modelling, unpublished) has a question, Let $(X,Y)^T$ be a bivariate random variable with joint ...
65 views

### How to determine uncertainty of data from a bayesian posterior distribution

I am a bit confused as to how we determine the uncertainty of a set of data from Bayesian Analysis. In my specific case, I am asked the following: Assume $f(x,x_0)$ as the correct model for the ...
Suppose I have data $y$ (N observations) which follows a normal distribution: $y \sim N(\alpha+\beta*\mu,\sigma^2)$ while $\alpha$ and $\beta$ are known parameters. I want to update $\mu$ and the ...