Tagged Questions

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.

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0
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0answers
16 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%
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1answer
15 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 ...
2
votes
1answer
42 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 ...
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0answers
22 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 ...
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0answers
41 views

Matlab: Unable to understand expectation operator $E[y_t]$

I have a time series model $y(t)$. I have conceptual problems related to the implementation of the Expectation operator in the following context How do I ...
4
votes
1answer
113 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
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1answer
22 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
120 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
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2answers
34 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
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1answer
34 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 $3.25$ ...
1
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0answers
13 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
57 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 ...
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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
90 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
59 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 ...
0
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0answers
12 views

$\alpha$ and $\beta$ values in SVM classifier

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 ...
6
votes
1answer
84 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
60 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
57 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
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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?
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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
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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 ...
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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
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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
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1answer
40 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
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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 = ...
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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 ...
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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
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0answers
35 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
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1answer
77 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) ...
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0answers
26 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
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2answers
49 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
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4answers
157 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
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1answer
89 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 ...
0
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1answer
78 views

PDF and CDF of sum of random variables with different distributions

This may sound too trivial but I am having difficulty to solve an assignment problem where I need to determine the distribution and density of a random variable $Z$ which is the sum of random ...
0
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0answers
40 views

Poisson GLM,Hessian matrix = the observed Hessian matrix

Assume a simple Poisson model with 2 unknown parameters (the intercept and the slope) Show that the expectation of the Hessian matrix = the observed Hessian matrix or equivalently the observed ...
1
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0answers
22 views

Predicted values and Prediction Intervals

Let the variable $x$ represents the age of a child and the variable $y$ represents the number of days a child absent from school in year 2000. A sample of 6 children give the following data: ...
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0answers
30 views

Loss and Payments

I am given that the amount of loss has a two-point mixture cdf, (55% and 45% weightage) which both follow a Gamma distribution. An insurance imposes an ordinary deductible of d and max. covered loss ...
2
votes
2answers
37 views

$X\sim \Gamma(p,a)$,find the two dimensional moment generating function of (X, ln X)

$X\sim \Gamma(p,a)$,find the two dimensional moment generating function of ($X, \ln X$) What I have done is $$M_{(X,lnX)}(t_{1},t_{2})=E(e^{t_{1x}+t_{2}lnx})=E(e^{t_{1}x}x^{t_{2}})=\int\int ...
2
votes
2answers
28 views

Scales of Measurement

when we use the term " scales of measurement", what do we mean by scale by Measurement ? As far i know, measurement denotes "a value" and scale denotes "the unit" of the value. So if i say, ...
0
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0answers
18 views

Separating variance due to treatment from variance due to sampling units

Consider a dancing competition where dancers are given a score between 1 and 100. Several teams participate in the competition, and each team gives several different performances. For each team, the ...
0
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0answers
6 views

UMP test for two different distributions

My question: UMP test for H0: X~u(0,1) vs H1: X~Exp(1) My attempt : By nayman pearson lemma The best critical region is Y >= c Where Y has Irwin-Hall distribution (sum of uniform distribution) and c ...
1
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1answer
48 views

Need help understanding Sufficient Statistics and using the formal definition

Let $X = (X_1, X_2, . . . , X_n)$ be a random sample from $Poisson(\theta)$. Use the factorization theorem to find a sufficient statistic $T(X)$ and then use the formal definition of sufficiency to ...
1
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1answer
23 views

Statistic calculation (Conversion from one unit to another)

I could get the mean using the formulae but not the value of SD and IQR from using the formulae. What is the problem? Thanks
0
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0answers
29 views

Statistic T-Test & T-table

Hi can anyone help me with this question . Thank you! I know that for part (a) degree of freedom is 13. But how do I use the t-table to answer (b) and (c). The t-table is below