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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.

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Simulation of the movement of a particle in three dimensions [on hold]

Could you help me with this? Write a function in R that describes the movement of a particle in a space in three dimensions. Starting from the point (x0, y0, z0) it moves as follows: In each step: ...
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60 views

Find $P(A^2 < B)$ where $A$ and $B$ are independent and uniformly distributed $\mathrm{Unif}(0,h)$, $h > 0$

I solved it two ways and in both the cases the answer is different and different from the actual answer. Approach 1: Since, $A$ and $B$ are independent, we can find the joint distribution of $AB$ ...
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0answers
12 views

Probit Hypothesis Test: $H_0: \beta_1 \geq 1$

Problem Given the output of a probit model and no knowledge of the sample data: ...
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1answer
26 views

Intensity function in Poisson random effect model

I have a somewhat general question about intensity functions in Poisson random effect models. Consider the Poisson random effects model in which conditional on a random effect $u$, an individual ...
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1answer
43 views

Bayesian posterior for Geometric Distribution

I have the following homework problem I am trying to solve for but am stuck with the posterior part. Note the the geometric distribution is a discrete distribution that has a probability mass function ...
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9 views

two-parameter Pareto distribution with known A [duplicate]

I am trying to solve the following problem. Any help would be great: Scores are distributed as a two-parameter Pareto distribution with a=3 Scores for 3 groups are as follows: Group A has expected ...
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0answers
11 views

Minimizing error is always good? [on hold]

I've got this question raised by my teacher that has been bugged me. Usually, we use learners in ML to minimize the classification error. On what situations minimizing the error is not the best ...
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0answers
27 views

Maths behind `geom_line()` in R [on hold]

I'm looking to fit a curve that ideally looks like a sigmoid curve. I can do this and get the sigmoid with geom_line(). However, I would like to know the ...
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20 views

How to merge few types of variables to one explanatory variable

so I have a data set of bike rentals in Washington D.C. Some of my variables are factors and some are numerics and continuous. I uploaded an image of a sample of my dataset so it will be easier for ...
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45 views

Critical region of distribution $f(x;\theta) = \theta x ^{\theta -1}$

I have been asked to find the critical region of the distribution given by $f(x;\theta) = \theta x ^{\theta -1}$ under the hypotheses $H_0: \theta = \theta_0 $ and $H_1:\theta < \theta_0.$ Show ...
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24 views

When calculating sum of observation in Bayes Theorem, why do we remove one outcome?

relatively quick question regarding this course question: Hearing about your brilliant success in working with M&Ms, Mars Inc. transfers you over to the Skittles department. They recently have ...
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Finding the UMVUE of $\theta^2$ where $f_X(x\mid\theta) =\frac{x}{\theta^2}e^{-x/\theta}I_{(0,\infty)}(x)$

Let $X_1, X_2, . . . , X_n$ be iid random variables having pdf $$f_X(x\mid\theta) =\frac{x}{\theta^2}e^{-x/\theta}I_{(0,\infty)}(x)$$ where $\theta >0$. Give the UMVUE of ${\theta^2}$ I ...
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1answer
43 views

Bayes estimator with weighted Loss

I have been working through a wide variety of problems involving Bayes risk and loss functions and I couldn't immediately solve the following From "The Bayesian Choice", Consider $x \sim N(\...
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44 views

Calculate a confidence interval of 88% for the difference in proportions

A survey of 400 men and 400 women in a certain city showed that 270 men and 240 women favor a certain proposition. Calculate a confidence interval of 88% for the difference in proportions between men ...
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Let X be the total score on the two dice and let Y be the number of times Bobo roll a one [on hold]

Bobo roll two dice. Let $X$ be the total score on the two dice and let $Y$ be the number of times Bobo roll a one. Find: Var($X$) Var($Y$) Var($XY$) Determine whether $X$ and $Y$ are independent or ...
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Interchange of differentiation and summation [migrated]

I came across an example about interchange of differentiation and summation. Can anyone show me how to prove the equation in the picture? Thank you!
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0answers
11 views

Find peak hour factor (Traffic Engineering) [on hold]

A highway section has been observed to be highly congested during peak hours. Being a 'traffic Engineer, you need to analyse the existing characteristics of traffic stream.. Traffic data related to ...
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1answer
73 views

Some questions about exponential families

Regarding the book The Bayesian Choice I understand most of chapter three on exponential families, but there are two parts I have trouble understanding. The first is Consider$$f(x|\theta)=h(x)\...
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24 views

Calculate $R^2$, $R^2_{adj}$, and F-statistic from $\text{R}$ model summary

I am given the full model, $M_{\tt f}$, with the regression line $$ {\tt response} = \beta_0 + \beta_1{\tt A} + \beta_2{\tt B} + \beta_2{\tt C} + \beta_4{\tt D} + \beta_5{\tt E} + \beta_6{\tt F} + ...
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Understanding the results of a Difference in Differences Regression? [closed]

I have just run a D-I-D regression to analyze the impact of a metro line on Property prices. Trying to understand what the different co-efficients mean.
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1answer
54 views

Uniform Distributions in R^d [closed]

R ~ Uniform (0,1) U ~ Uniform $(S^{n-1})$ (surface of an $n$ sphere) $R \perp U$ X $\stackrel{d}{=}$ RU, what is the distribution of X? This was asked to me as an example of a question that might ...
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43 views

Cumulative distribution function of a squared laplace random variable

I am trying to calculate $F_Y(x)$ (CDF) of $Y=X^2$ where $X$ is a random variable of Laplace Distribution $f_X(x) = \frac{1}{2}e^{-|x|}$ (let's take a simple case when parameters $\mu=0$ and $b=1$). ...
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30 views

How can we use the basic statistical analysis in R to answer these questions?

I have come across this task which refers to the the simple statictical tests, such as Student's T-test, binomial test and chi-squared.Also this task can be done with the help of descriptive ...
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1answer
27 views

How to derive the noninformative prior for location parameters and scale parameter?

I am reading this paper, in it: I have a lot of confusion reading it, I will list it one by one: Let $X$ be distributed as $f(x-\theta)$, which is a location invariant density. Q1: The sentence <...
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Write function ecdf [closed]

My question is about ECDF Write a function ecdf that calculates the empirical cdf of a given numeric vector at the point t. The default value for t should be 0. You can assume that t is also a ...
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0answers
24 views

Dirichlet distribution as conjugate prior to Multinomial distribution

I stumbled upon the following exercise: Show that Dirichlet distribution with parameter $\alpha$ is a conjugate prior to the Multinomial distribution as likelihood. Derive the parameters to the ...
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1answer
38 views

UMP Test of $H_0 : \theta \leq 0.1$ vs. $H_1 : \theta \gt 0.1$ for iid Geometric Random Variables

Consider $90$ iid geometric random variables having parameter $\theta$ (and thus mean $1/\theta$), and a UMP test of the null hypothesis that $\theta \leq 0.1$ against the alternative that $\theta ...
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1answer
39 views

I am confused as to which nonparametric procedure I should be performing on my data

My question reads: "A computer laboratory manager was interested in whether there was a difference in functioning time for three different branded battery packs for laptop. The manager took a random ...
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2answers
110 views

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 $x_2>-2$ ...
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1answer
61 views

Check if log-likelihood function is correctly derived

This question is a continuation of this one. By guesswork, I found out that $\vec{\theta}=(5.2,5.3,1.0)=$ $(A,B,C)$ was a good guess that made my model $$y_i=A\sin\left(\frac{x_i}{B}\right)+C\...
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1answer
42 views

How to derive joint CDF Gumbel distribution

If you have 3 random variables: $X$, $Y$, and $Z$ and they have independent Gumbel distribution. $A$, $B$ and $C$ are three discrete random variables that are functions of $X$, $Y$, and $Z$ as per the ...
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1answer
31 views

Simple Z-Score question dealing with normal mean and standard deviation I keep getting incorrect

The question below is simple, however, I got the question wrong despite following a basic formula I have been using for a while now. Here's the question: For applicants who actually entered medical ...
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1answer
56 views

Convergence of $U_n=\frac{1}{\sqrt{2n\sigma^2}}\left(\Sigma X_j-\Sigma Y_j\right)$ - central limit theorem

Suppose that $U_n=\frac{1}{\sqrt{2n\sigma^2}}\left(\Sigma X_j-\Sigma Y_j\right)$, where $X_1,X_2,\ldots$ and $Y_i,Y_2, \ldots$ are i.i.d. sequences of random variables with mean $\mu$ and variance $\...
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2answers
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Prove convergence in distribution for n times the minimum of an unknown positive distribution

Let $Z_1, Z_2, ...$ be independent and identically distributed random variables with some density $f$. Suppose that $P(Z_i > 0) = 1$, and that $$ \lambda = \lim_{x\to 0} f(x) > 0$$ Let $X_n = ...
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0answers
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Prove bi-directional relationship between convergence in distribution and convergence of probability mass functions

Let $X$ be a random variable that is positive and integer-valued. Let $X_1, X_2, ...$ also be random variables that are positive and integer-valued. Prove that $X_n$ converges in distribution to $X$ ...
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1answer
41 views

Finding joint support of $(XY,X/Y)$ where $(X,Y)$ has joint pdf $1/x^2y^2$ for $x,y\ge1$

$X$ and $Y$ are random variables with joint pdf $$\frac{1}{x^2y^2}\qquad,\, x\ge1,y\ge1$$ Set $$U=XY, V=X/Y$$ Explain why the joint range of $U$ and $V$ is given by: $$\{(u,v):v\in(0,1),u\ge1/v\} \...
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2answers
154 views

Testing whether $X\sim\mathsf N(0,1)$ against the alternative that $f(x) =\frac{2}{\Gamma(1/4)}\text{exp}(−x^4)\text{ }I_{(-\infty,\infty)}(x)$

Consider the most powerful test of the null hypothesis that $X$ is a standard normal random variable against the alternative that $X$ is a random variable having pdf $$f(x) =\frac{2}{\Gamma(...
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Why divide by 1-leverage?

I'm reading about resampling methods, and specifically leave-one-out cross-validation. I understood the method, and how to calculate the estimate of the test MSE (Mean squared error): In the setup ...
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0answers
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Which test to use from a paired data that has only 4 cases of information from each group

I have a question from an exam: A Statistics Professor believes that adding videos of statisticians consulting on applied problems to her standard instructional material will help students solve ...
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1answer
34 views

How to prove the concentration equality for standard normal?

The following inequality is given in some of Yale's online lecture notes $$P(|Z|>x) \leq 2 \sqrt{2 \pi} \phi(x)$$ Where $Z \sim N(0,1)$ with density $\phi(x)$. They call it a concentration ...
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Confused with What Kind of Test I Should be Using

I have a question from an exam: The chef rates the taste quality of 5 different brands of anchovies. The brands came packaged in both a jar and a can. The chef rates 10 combinations of brand/...
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1answer
29 views

How to get standard deviation when the only given information is sample mean and p-value

I have a question for an exam: You read a journal article on TOTAL-cholesterol, HDL-cholesterol and LDL-cholesterol from a study of n=100 patients where TOTAL-cholesterol = HDL + LDL cholesterol. ...
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2answers
49 views

Calculating a probability based on a joint distribution between a Uniform random variable nested within a Uniform(0,1) random variable

Let $X_1 \sim Uniform(0,1)$, and $X_2 \sim Uniform(0, x_1)$, where $x_1$ is the realized value of $X_1$. Find $P(X_1 + X_2 \geq 1)$. I know that I need the joint distribution of $X_1$ and $X_2$. $...
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1answer
56 views

Profit maximization problem using linear regression

I'm currently on a university assignment where I'm stuck more or less in the middle. I have to answer the following problem: Suppose you are interested in estimating the production function for ...
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24 views

A question about sample partial correlation coefficient and multiple correlation coefficient

Question: My problem: All possible formulae of Multiple and Partial Correlation Coefficient I know :- But I am not sure, which one to use to know about the situation or condition mentioned in the ...
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1answer
27 views

Bonferroni interval - quick example calculation

Problem statement: Calculate the Bonferroni interval for any pair of means $\bar{y}_{.j},\bar{y}_{.k}$ with $I$=10 groups with equal sample size 30 in each group. Write this as a multiple of $s$. ...
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A problem about Partial Correlation Coefficient

Question: Prove that for a set of p variables, if all the simple correlation coefficients are negative, then all the partial correlation coefficients of all orders are also negative. My problem: I ...
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79 views

Finding the UMP size $0.1$ test with $U\sim\text{Unif}(\theta, \theta+1)$

$U$ is a uniform $(\theta, \theta+1)$ random variable, where where $\theta\in(−0.5,0.5)$. Consider testing $$H_0:\theta\geq0$$ $$H_1: \theta \lt0$$ (a) Give the test function of a ...
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1answer
68 views

A question about Trivariate Normal Distribution

Question: Let $(X_1,X_2,X_3)\sim N_3\left[\mathbf0, \begin{pmatrix}1&\rho_{12}&\rho_{13}\\\rho_{12}&1&\rho_{23}\\\rho_{13}&\rho_{23}&1\end{pmatrix} \right]$ Show that ...
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1answer
24 views

Two- Sample T test on Employment Data

I'm trying to conduct a two sample t-test on this data on food and drink workers in the Seattle MSA to see if there is a mean difference in levels of employment before and after the enactment of an ...