A routine question from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for self-study questions.

learn more… | top users | synonyms (1)

0
votes
0answers
7 views

Data set with negative silhouette

I want to construct data set 𝐷 in 2 dimension, with a clustering {𝐶1, 𝐶2} computed by k-means with the property: which full fills the condition: There exists a point $𝑜∈𝐷$ with a negative ...
0
votes
0answers
11 views

Conceptual question on correlation matlab and implication [on hold]

Let, x = [1 0.9 0.1 -0.3]'. The formula for creating correlation matrix is E[x*x']. I have confusion related to implementation ...
1
vote
0answers
6 views

A question about Dickey-Fuller Unit-Root Test

I am reading Dickey-Fuller Unit-Root Test in Time Series Analysis with Applications in R by Cryer and Chan and have trouble understanding some discussion on equation (6.4.1). So they took this ...
0
votes
0answers
8 views

Kernel matrix is a covariance function

How to prove that the kernel matrix is actually a covariance matrix?
0
votes
0answers
27 views

Expectation Maximisation Algorithm: Understand through numeric example

I am trying to learn machine learning concepts through online materials. I just studied tutorial on Expectation Maximisation algorithm. I thought one numerical example can make better understanding. ...
0
votes
0answers
13 views

Deriving the maximum likelihood for a generative classification model for K classes

In Christopher Bishop's book "Pattern Recognition and Machine learning", there is the following question: Consider a generative classification model for $K$ classes defined by the prior class ...
3
votes
1answer
41 views

Conditional independence iff joint factorizes

I have proven that: $X⊥Y|Z\ {\rm iff}\ p(x,y|z)=p(x|z)p(y|z)$ for all $x,y,z$ such that $p(z)>0$. The next question is to prove an alternative definition: $X⊥Y|Z$ iff there exist functions $g$ ...
1
vote
1answer
47 views

Negative Binomial Distribution R

This question was given in class and I was wondering how to do this in R: "Sixty percent of a large lot of old spark plugs are still usable, and they can be individually tested to determine this. Let ...
0
votes
1answer
27 views

SVM parameters clarification

James et al. in An introduction to the statistical learning (p. 351) claim that the solution to the support vector classifier problem involves only the inner products of the observations. They ...
1
vote
0answers
24 views

What statistical analysis to use?

What statistical analysis should I use if I have 2 groups of subjects (high and low comprehenders) which are divided into 3 subgroups according to text genre (poetry, short story, drama) and subjected ...
2
votes
1answer
54 views

Why does a goodness of fit test use the chi square distribution rather than the hypothesised distribution?

This is a homework(-like) question. I know the answer but don't understand it. If we were to answer the question "Are 5 different groups of mammals equally common?", what test would you perform? ...
2
votes
1answer
64 views

t test with log transformation

One of my variables to be compared in a t-test is normally distributed, while the other is non-normally distributed. What test should I use? I thought I should do a reflect log10 transformation on the ...
0
votes
0answers
6 views

How to determine if a U chart or a C chart to be used

This is regarding theory of attribute type control charts.In a question it is given data for the number of non confirmities per 1000 meters of wire. I have to calculate control limits for a ...
0
votes
0answers
25 views

How to determine the sample size, if standard deviation, population mean, sample mean and precision is given?

Determine the sample size if sample standard deviation is 6, population mean : 25, sample mean = 23 and the degree of precision is 99%
0
votes
1answer
19 views

Statistics - (bivariate data) Planning an Inquiry

I have to conduct a statistical inquiry that is representative of a population. You have to choose from a list of situations, and my choice was to measure the weight and length of carrots. The ...
3
votes
1answer
53 views

Bayesian Estimation: Bernoulli and Quadratic Loss Function

I am trying to understand a solution to this problem (I am a very beginner in Bayesian statistics) and I am terribly confused so I would appreciate it if someone could explain to me how exactly this ...
0
votes
0answers
24 views

How to check $H_0$ hypothesis using Pearson's criteria?

How to check hypothesis by using Pearson's criteria, that $H_0:$ random variable $X$ is normally distributed given that $k=7$ (count of intervals) and $\alpha=0.1 $ (significance level). I do ...
5
votes
1answer
117 views

How to calculate $P (|X − Y | ≤ 1/6)$? [duplicate]

$f_{X,Y} \left( x, y \right) = 1\quad \text{for}\quad 0≤x≤1,\ 0≤y≤1 $ and $0$ otherwise. How to calculate $P \left( |X − Y | ≤ 1/6 \right)$?
3
votes
1answer
24 views

Hypergeometric approximated Normal/Gaussian distribtuion

A large lecture theater has 270 seats, 24 of which can accomodate left-handed students. Suppose it is known that 14% of people are left-handed. One class held in the theater has 205 students. (a) ...
5
votes
1answer
123 views

Probability of getting the correct direction, given you get the same answer

A town is composed of $2/5$ out of town couples and $3/5$ in town couples. If a couple is from out of town, the probability that the husband and wife will give you the correct directions ...
4
votes
2answers
36 views

Population is normal with known variance and mean. Sample size is small. Which case?

Given a population (normal distribution) mean and variance and a sample set with n<30 values, how should I perform hypothesis testing. My professor told me that I should be using the t-test for ...
0
votes
1answer
36 views

What is the formula for a normal-theory confidence interval of the mean?

A psychologist is collecting data on the time it takes to learn a certain task. For $55$ randomly selected adult subjects, the sample mean is $10.5$ minutes and sample standard deviation is $3.25$ ...
0
votes
0answers
15 views

Conditional and joint pmf of sequences of random variables

I have random variables $X_1...X_N$ which are Poisson($\theta$) distributed. I also have inclusion indicators $Y_1...Y_N$ which are Bernoulli($\pi$) distributed. These indicate whether $X_i$ is ...
1
vote
1answer
73 views

Deriving the maximum likelihood for the parameters in linear regression

Notation: $\textbf{w}$ is an M-dimensional vector of parameters (including the bias parameter), $\textbf{x}_n$ is an M-dimensional vector of the features of each training example, $\textbf{t}$ is an ...
0
votes
0answers
27 views

Correct formula for this example

Population size is $N =10000$. The standard error of proportion estimation must not be larger than $0.02$, i.e., $sh(p)\le 0.02$. In a previous study, the confidence interval of $p$ was between $o.25$ ...
2
votes
1answer
93 views

Convergence of $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$ if $X_1, \dotsc , X_n \sim U(0,1)$

$X_1,X_2,\dotsc ,X_n$ are independent, uniformly distributed random variables on the interval $[0,1]$ The question is the convergence of the sequence: $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$. ...
2
votes
1answer
64 views

Maximum likelihood estimator for minimum of exponential distributions

I am stuck on how to solve this problem. So, we have two sequences of random variables, $X_i$ and $Y_i$ for $i=1,...,n$. Now, $X$ and $Y$ are independent exponential distributions with parameters ...
6
votes
1answer
85 views

Random variables with some properties (conditional expectation)

I am looking for two random variables which fulfills the following two things: a) $\mathbb E(X|Y)<\infty$ and $\mathbb E(Y|X)<\infty$ b) $E(X|Y)> Y$ and $\mathbb E(Y|X)>X$ a.s Here is ...
1
vote
1answer
72 views

In a two-way ANOVA, how can the F-statistic for one factor have a central distribution if the null is false for the other factor?

Consider the two factor additive ANOVA model $$\begin{align} X_{ij} &=\mu_{ij}+e_{ij} \\ \mu_{ij}&=\mu+\alpha_i+\beta_j \end{align}$$ where as usual $\sum_{i=1}^a \alpha_i=0$ and ...
1
vote
1answer
59 views

Sufficient statistics for $\mu_1 - \mu_2$

If $ X_1, ..., X_n$ is a random sample from $ X \sim N(\mu_1, \sigma^2)$ and $Y_1,..., Y_n$ is a random sample from $Y \sim N(\mu_2, \sigma^2),$ if the samples are independent and $ \sigma^2$ is ...
3
votes
1answer
76 views

Explain confidence intervals in simple terms

For one newly handling statistical analysis, please can you explain in the simplest of terms, with an example, what is a confidence interval?
0
votes
0answers
39 views

How to determine the pdf from the sum of different distributions

Consider a discrete random variable $Z(t) = \phi_1Z(t-1) + \phi_2Z(t-2) +\dots+\phi_pZ(t-p) + \mu(t)$ $Y(t) = Z(t) + \eta(t)$ where $\mu$ is a zero-mean deterministic nonlinear signal following a ...
0
votes
1answer
29 views

null and alternative hypotheses

A group of 50 complete a national fitness test and get a mean score of 80 out of 100. The national average is 72 with standard deviation 6. Can we conclude the group of 50 is fitter than the national ...
-1
votes
1answer
51 views

Indepent variables and these functions [closed]

Random variables $x_1, x_2,...,x_n$ are independent. Then I want to show whether these functions $$y_1=f_1(x) \\ y_2=f_2(x) \\ ... \\ y_n=f_n(x)$$ are independent or not . How to prove this?
1
vote
1answer
46 views

Conceptual Question: Autocorrelation of autoregressive process

An AR(1) process: $X_t = c+\theta X_{t-1} + \epsilon_t$ where $\epsilon_t$ is a zero mean white Gaussian noise. The Autocorrelation matrix is expressed by the formula mentioned in the Wikipedia ...
2
votes
0answers
23 views

Regression variable conversion

There is a question that I cannot solve. They may be solved by variance and covariance but I couldn't. So I thought there should be another way to solve. Question: A researcher has a sample of 43 ...
1
vote
1answer
45 views

Developing a self-study plan

I see that some previous questions have danced around this topic, but I can not find any answers that truly hit on my scenario. High Level Goal: Develop a sequential self-study plan aimed at ...
0
votes
0answers
15 views

Statistical Treatment in Yes/No/Maybe questionnaire

I'm currently in the midst of a research about wired LAN and WLAN for my english subject. My respondents would be 15 household users and 15 internet cafe owners. My reason for my research is to know ...
0
votes
0answers
22 views

How to find normal quantiles?

A social psychologist interested in eating behavior wanted to divide students into four groups based on their eating proclivities. The four groups were those who were restrained eaters, moderately ...
0
votes
1answer
17 views

Log Linear Models: Interpretation when None Fit

This is question 9.6 from Categorical Data Analysis by Alan Agresti (Wiley, 2013). The question asks us to find a Log Linear with the best fit for a 2x2x2 contingency table. The following are the ...
1
vote
1answer
43 views

Conceptual questions: Variance of a process

Wikepedia, at Variance of Autoregressive model, mentions an expression of variance for an AR(1) process. I am learning signal processing (beginner level) and facing difficulty in understanding some ...
1
vote
1answer
32 views

Derivative of power spectral density

The power spectral density (PSD) of an AR(p) model excited by a white Gaussian noise input $u(t)$ of variance $\sigma_u^2$ is $P_{xx}(f:\theta) = \frac{\sigma_u^2}{|A(f)|^2}$ where $\theta = ...
1
vote
1answer
34 views

Help setting up a Bayes rule problem

I am relatively new to using Bayes rules for continuous variables and am having trouble setting up part of the formula and am looking for help. The example I am trying to work through is the ...
1
vote
0answers
21 views

null hypothesis confusion

Experts argue that at most 30% of schools pupils benefit from homework. A sample is taken. Write down null and alternative hypotheses. I would have thought that the null would be that the number of ...
0
votes
0answers
36 views

Getting Sample size

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between \$35,000 and \$50,000 (Hint: Refer to the last slide of your Chapter 8 ...
3
votes
1answer
78 views

Problem with urn

I'm reading Thinking fast and slow and there's this problem I cannot get a correct answer. Here it is: Half the marbles are red, half are white. Next imagine a very patient person (or a robot) ...
1
vote
0answers
30 views

Hypothesis testing with Neyman–Pearson Lemma

I have hypothesis: $H_0: X\ \sim\ \mathcal{N}(-1,\,1)$; $H_1: X\ \sim\ \mathcal{N}(-9,\,9)$. Also I have significance level $\alpha = 0.2$. I'm checking them by Neyman-Pearson Lemma. 1) Find ...
2
votes
2answers
52 views

Derive the LLN for a certain sequence

I have a sequence of dependent random variables $X_1, X_2...X_n$. Each RV is correlated with two other RVs and uncorrelated with the others.The ones that are correlated satisfy the condition ...
1
vote
4answers
159 views

How to choose the null and alternative hypothesis?

I'm practicing with the hypothesis test and I find myself in trouble with the decision about how to set a null and an alternative hypothesis. My main issue is to determine, in every situation, a ...
3
votes
1answer
96 views

How to find set of directions in Stahel-Donoho outlyingness measure?

Currently I’m trying to understand and use the Stahel-Donoho outlyngness measure. But unfortunately I’ve got a problem in the part where one is taking the maximum over the set of directions. I found ...