Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [self-study]

A routine exercise 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.

0
votes
1answer
45 views

What is Intraclass Distance?

For an assignment I have to compute the intra-class distance and use it as an objective function to select features. This is for the MNIST dataset. While I have a fairly good handle on other aspects ...
1
vote
0answers
17 views

Probability Two Independent Samples of Different Size Have Some Intersection

I've been working on generating a probability rule for taking two random samples without replacement and finding a given amount of overlap between the two. So far I've worked through simple cases ...
1
vote
0answers
14 views

Defining a posterior for poisson distributed data

I am trying to make a formulation of a posterior for a problem with this structure. For a chemistry experiment we have completed two rounds. The first round lasted for 4 months. In this round two ...
0
votes
1answer
30 views

Statistics Homework Help [closed]

Not sure how to tackle this question, can someone help me? A team of medical researchers carried out a study among swimmers to investigate a possible link between exposure to chlorinated swimming ...
0
votes
1answer
25 views

Expectation / Summation inequality with multiple indices

Part of a solution to an exercise in the book Stochastic Processes From Application to Theory (exercise 87) is the following summations: $$\sum_{i\ge1}P\left(I_i \ge i \right) = \sum_{j \ge i\ge1}P\...
1
vote
1answer
28 views

Finding the CDF given marginal PDF's; setting bounds

In this question, I'm having a hard time understanding how specifically to set the bounds for the CDF. Let $X$ and $Y$ be independent variables. Find the CDF of $W=Y/X$ using the marginal PDFs ...
7
votes
0answers
60 views

MLE, regularity conditions, finite and infinite parameter spaces

The problem I have is in figuring out why the MLE is no longer consistent in countable parameter spaces under conditions specified below. The set up is as follows: we are consider a parameters space ...
0
votes
0answers
15 views

Removing coefficients from multiple regression analysis

0verview I am undertaking a study where we analysing the fine details of two multiple regression equations. Multiple regressions were carried out for the months of February and August 2017, with ET ...
-1
votes
1answer
40 views

Deriving standard normal distribution from a statistic involving normal and uniform random variables

I tried deriving distributions of numerator and denominator separately. But found that there is no closed form. I have no clue on how to show that Z is standard normal.
0
votes
1answer
13 views

How to deal with unequal variances in repeated measures ANOVA

Angry Birds is a video game in which you fire birds at pigs. A (fabricated) study was set up in which people played Angry Birds and a control game (Tetris) over a two-year period (one year per game). ...
0
votes
0answers
14 views

Analyzing and interpreting main effect in repeated measures ANOVA

Angry Birds is a video game in which you fire birds at pigs. A (fabricated) study was set up in which people played Angry Birds and a control game (Tetris) over a two-year period (one year per game). ...
1
vote
0answers
28 views

Prove limiting distribution goes to stationary distribution: $\lim_{t\to\infty} \pi_{j}(t) = \overline{\pi}_{j}$

This is a problem I'm struggling with on continuous-time Markov chains. Here, we are considering a continuous Markov process with phase space $\{1, 2\}$ (there are only two states). Moreover, $\...
5
votes
1answer
95 views

How to improve this time series model?

I am trying to fit a time series model for household data which is a time series variable. Initially my data looks like this, Since the data does not seem to be stationary I differenced the data. ...
0
votes
1answer
53 views

A question about hypothesis testing [closed]

Question I am actually finding no clue how to start with this sum. Please help. Thank you.
0
votes
0answers
8 views

What statistical test should I use for my survey question?

I am a complete novice to statistical things and would appreciate your help. Given that I am running a survey between Males/Females and my question is: I am interested to stay in hotels<1 day, ...
1
vote
1answer
24 views

Why do we use quadratic form for random vectors? [closed]

I am studying linear regression. I have studied this in the past, but this is my first time exposing myself to the matrix form of multiple linear regression. My matrix algebra/linear algebra skills ...
0
votes
0answers
13 views

How to interpret regression coefficients when each predictor variable contains different categories

Overview: I have conducted two types of statistical analysis using both linear regression and multiple regression. Overall, there were two observation periods, and the idea is to gauge if the rate ...
2
votes
0answers
35 views

Sum of Random Variables — An Example with R [closed]

So I was trying to simulate these formulas from my lecture with R. $$E[\bar{X_n}] = \mu_x\text{, where $X_i \sim i.i.d$}\\Var(\bar{X_n}) = \frac{1}{n}*\sigma^2_x$$ My code in R: ...
3
votes
1answer
24 views

Negative Binomial Substitute for Poisson Applied to NYC Crime Data

I'm reading these questions and answers (http://study.sagepub.com/sites/default/files/chapter4.pdf) and am confused about 4.2.4 - 4.2.6 I agree that the Poisson model developed earlier is not a good ...
0
votes
1answer
11 views

Markov Chain Question/Notation Confusion

Show that if $(X_n)_{n \geq 0}$ is a discrete-time Markov chain with transition matrix $P$ and $Y_n = X_{kn}$, then $(Y_n)_{n \geq 0}$ is a Markov chain with transition matrix $P^k$. I am a little ...
-1
votes
1answer
21 views

Some help interpreting posterior plots

I needed some help interpreting and comparing the plots that I created. I'm not really sure what is the most important thing to talk about when comparing these plots. I know for these plots that the ...
1
vote
0answers
38 views

Whats the most appropriate test: Anova, multiple regression, or linear regression? Confused!

Overview As part of a group practical activity, we collected phenological data from deciduous oaks trees which were pooled into a large database (see the data frame below). Parameters Measured ...
0
votes
1answer
19 views

Recursion in Probability questions

I don't quit understand the explanation for recursion here. Why is there firstly the need to have i on the numerator for the first underlined bit? Would it be because of combinatorics? So the second ...
0
votes
1answer
32 views

Conditional expectation of two independent RV

The expectation of the product of two independent random variables $X$ and $Y$ is the product of the expectations: \begin{align} E(XY) = E(X)E(Y) \end{align} Let's add another random variable $Z$ in ...
1
vote
1answer
33 views

Why covariates are used in Latent class analysis (LCA)

I am trying to learn this relatively new statistical technique LCA. In literature i saw that for some LCA models, covariates are used. I am having a difficulty to understand why additional covariates ...
2
votes
2answers
72 views

Calculate E[X] from incomplete data?

The exercise I'm doing describes the random variable $X$ as the following ...
0
votes
2answers
32 views

The difference between our sample estimate and the true population value is known as: [closed]

The difference between our sample estimate and the true population value is known as: A. Mean Value B. Standard Deviation C. Standard Error D. Variance With explanation please
0
votes
1answer
33 views

maximum likelihood of binomial distribution over number of outcomes (k) with known probability (p)

I've tried to find the answer to this question, but have been unsuccessful I'm curious if there is a way to use a ML estimator to find the optimal number of outcomes ($k$) to maximize the binomial ...
1
vote
1answer
55 views

Elicit a Proper informative priors

I need help with eliciting,deriving and plotting two proper informative prior. One with mean and standard deviation Another with LQ, UQ and Median Is the first one using a normal distribution while ...
0
votes
1answer
25 views

Why $P(BB|BG \cup BB) = \frac{P(BB)}{P(BG \cup BB)}$?

I have the following question: Determine the probability both children are boys if I have 2 children, the elder is a boy? Then the textbook says: Take BB, BG, GB, GG as the possible outcomes (first ...
1
vote
1answer
31 views

why are there loss functions AND auxiliary loss functions?

I am a beginner reading neural networks. I wonder why there are loss functions, and then there are auxiliary loss functions. (By definition, 'auxiliary' would mean supplementary, help, support). My ...
0
votes
1answer
31 views

Moving Average Method

Suppose I have data for 6 months: $2,5,1,9,3,4$. If I calculate 3 months moving average, then from this data, I get two average $2.667(=\frac{2+5+1}{3})$ and $5.333(=\frac{9+3+4}{3})$. But if I have ...
0
votes
0answers
10 views

Scheffe's S Method - help with finding the absolute value of l

I am trying to understand Scheffe's S Method and how the absolute value of l is found. In the example I am reading, the absolute value of l is |-.836| but I have absolutely no idea how this value was ...
2
votes
1answer
64 views

variance of nonparametric estimator of mean

I'm having some trouble with understanding how to calculate the variance of a non-parametric estimator. The example comes from Wasserman's "All of statistics book" Let $X_1, \ldots,X_n \sim \text{...
1
vote
1answer
40 views

Distribution of a one realization of a stochastic process [closed]

Suppose $X$ is a stochastic process such that $X(t) \sim N\left(\mu(t), \sigma^2(t)\right)$ for all $t$ and $\mu$ and $\sigma$ are some smooth functions and we are given one realization of this ...
-1
votes
1answer
30 views

Estimation of an exponential parameter

I´m trying to figure out the pdf $f_\min(X_i)$ of $\min(X_i)$, where the distribution of the sample $X_1,...,X_n$ is $\mathcal{E}xp(\lambda)$, where $\lambda$ is the unknown parameter. I tried with ...
0
votes
0answers
32 views

Order statistics of a single r.v

I have trouble understanding the following question: We have N i.i.d random variables from the uniform distribution between 0 and 1. If N=1, what is the probability that the n^th order statistic ...
9
votes
2answers
469 views

Probability of $X_1 \geq X_2$

Suppose $X_1$ and $X_2$ are independent geometric random variables with parameter $p$. What is the probability that $X_1 \geq X_2$? I am confused about this question because we aren't told anything ...
1
vote
0answers
31 views

The Linear Discriminant Analysis Rule

Given there are two classes A and B and the prior probability of belonging to $ A = Na/N $ and $B = Nb/N $, I want to show that the linear discriminant analysis rule classifies an observation x to ...
1
vote
0answers
29 views

When is the pmf of the difference of two independent random variables symmetric in zero?

Consider the stepwise cumulative distribution function $$ \Delta(x; \lambda, \mu)=\sum_{j=1}^J \lambda_j 1\{x\geq \mu_j\} \hspace{1cm} \forall x \in \mathbb{R} $$ where $J<\infty$ $\lambda\equiv (\...
3
votes
0answers
27 views

Partitioned regression model: estimator of beta 1

below is an exercise that is really giving me a hard time, I believe that there is a simple way around it but I can not find it: Assume the correct regression model is Y = X$\beta$ + $\epsilon$ for E(...
2
votes
2answers
39 views

How to change in y variable having means, standard deviations, and correlation coefficient?

The following statistics have been obtained by using the data of money supply growth rate and inflation rate for the last 30 years. The average money supply growth rate, its standard deviation,...
0
votes
0answers
11 views

Formula for Power of Upper Tail Sign Test

Given Consider the upper tail $H_0: \theta \leq 0 \,\,\, \text{vs} \,\,\, H_A: \theta > 0$ sign test with the test statistic $B = \sum_{i=1}^n{\psi_i}$ where $\psi_i = \mathbb{I}(Z_i > \theta)$...
-3
votes
1answer
36 views

Statistics and Probability. Please show solution [closed]

Miss Romero noted that the mean scores of a random sample of 15 grade 8 students who had taken a special test were 80.5. If the standard deviation of the scores was 3.1 and the sample came from an ...
0
votes
1answer
31 views

Odds Ratio Vs. Risk Ratio

Relative risk, odds ratio, risk ratio, risk difference - these are all measures of the direction and the strength of the association between two categorical variables. Can I use any of these four ...
0
votes
1answer
29 views

Constant Variance Assumption in Linear Regression

It seems to me that the following plot of "Residuals Vs. Fitted Values" violates the assumption of constant variance, since for lower fitted values, there are fewer points whereas for higher fitted ...
0
votes
1answer
34 views

Simple Regression Question for Probability of Smoking

Variable smokes is a binary variable equal to one if a person smokes and zero otherwise. We estimate a linear probability model for smokes: $$\hat{smokes} = .656 - .069\log(cigprice) + .012\log(...
0
votes
1answer
34 views

Properties of Nonparametric Test Statistics $B$

Given Consider the upper tail $H_0: \theta \leq 0 \,\,\, \text{vs} \,\,\, H_a: \theta > 0$ sign test with the test statistic $B = \sum_{i=1}^n{\psi_i}$ where $\psi_i = \mathbb{I}(Z_i > \theta)$...
0
votes
0answers
13 views

Prior for precision tau on Normal distribution with unknown mean [duplicate]

I am working with prior distributions. I need to define a prior for tau precision $\tau=1/\sigma^2$ for a Normal distribution with unknown mean $\mu$. Likelihood for normal distribution below tau ...