# 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.

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### Two-proportion hypothesis test with variances unknown

"A group of test subjects are split into two groups. 1000 people are given a vaccine, and 15 of them get the disease. 800 people are given a placebo, and 60 of them get the disease. Test the ...
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### How to show in R, using a simulation, that when sampling from a normal distribution, the sample mean and sample variance are independent

What is the best way to show that when sampling from a normal distribution, the sample mean and sample variance are independent? I know the theory behind this result, I would like to show it using a ...
44 views

### F-Statistic and F-distribution [duplicate]

I am reading ISLP chapter 3.2 about multiple linear regressions. F-statistic seems like to be a statistic calculated per sample. But also we know that it is just and estimation for the stat on whole ...
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1 vote
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### Finding probability involving dependent random variables [closed]

Suppose train on line A arrives in time uniformly distributed between 0 and 4mins, train on line B arrives in time uniformly distributed between 0 and 6 mins, and furthermore the time interval between ...
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1 vote
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### Exercise involving Bayes' Theorem

Consider the problem During exam time, in a certain school, only 25% of the teachers warn their students in writing that they are not allowed to get up to ask questions during exam time. in writing to ...
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### Find $P(Y>\frac{5}{4})$ when joint pdf of $X$ and $Y$ is given

The joint pdf of $X$ and $Y$ is given as $f(x,y)$ = $\frac{1}{2x^2y}$ , $1<x<∞$ and $\frac{1}{x}<y<x$ Then find $P(Y>\frac{5}{4})$ Since the limits of $Y$ have $X$ in them, I am not ...
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### Asymptotic normality implies consistency

I'm trying without success to solve the following exercise in my econometric textbook: Show that $\sqrt{N}\left(\widehat{\beta_1} - \beta_1 \right) \xrightarrow{d} \mathcal{N}(0,a^2)$, where $a^2$ is ...
1 vote
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### How to manually evaluate a parameter estimate using the first few values of a time series?

I'm working on a problem (I paraphrase), Consider the $\text{AR}(2)$ model $$y_t=\alpha y_{t-1}-(1-\alpha)y_{t-2}+\epsilon_t, \hspace{1em} \epsilon_t\sim N(0,\sigma^2).$$ The conditional least ...
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1 vote
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### Deriving Sample Size for two samples t test

I am trying to figure out what sample size recommendations to make in this case when the samples have different sizes. Since their sizes are different the variance of each will be different. Suppose ...
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### What is the difference between sampling error and measurement error?

The terms sampling error and measurement error in statistics field are very relevant and have a paramount importance for data analysis and reporting.
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### Deriving the Distribution of Markov Chain Times

I am interested in learning how to derive the probability distributions for the Time to Absorption in Markov Chains (Discrete and Continuous). In the past, I have usually done one of the following: ...
28 views

### Identifying the alternate hypothesis [basic]

I was dealing with the following question: After a change management, a producer claimed that less than 5% of his flak jackets have production flaws. A sample of 200 flak jackets was randomly ...
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### $U$-statistics and their limiting distributions

Let $X_1,X_2, . . . ,X_n$ be i.i.d. observations from a continuous distribution $F$. Consider the parametric function $\mathbb{P}([\text{min}(X_1,X_2) > X3])$. Find the U-Statistics and its ...
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### What's the purpose by returning back the bad outliers from AdaBoost?

Assume that you having a matrix $X$ that holds both numerical and binary data. You plug in the data $X$ into AdaBoost and AdaBoost update the $X$ by only focusing on the rows that could not make a ...
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### Interpretation of PCA principal components

As a result of a PCA analysis with some initial correlated variables $X_1,..,X_k$ we often do a plot of the loadings to intepret the principal components: PLOT 1: Plot of the loadings: We call \$v^i,i=...
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### Apriori Algorithm confusion: difference between frequency and support

What is the correct way to calculate support? I have seen two different ways and I'm confused as a result. One way (say first approach) is explained https://en.wikipedia.org/wiki/...
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### LMM in SPSS for a medical treatment analysis (repeated measurements and nested structure)

For a statistical analysis of a medical treatment I want to use an LMM (linear mixed model) and am quite unsure on how to do that correctly, in particular in SPSS (which is the license I have obtained ...
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38 views

### Hypothesis Testing of categorical variables [duplicate]

CONTEXT Suppose i collected data sets from a survey over google form, my sample is consisting of 32 row with the age/sex/major of the person who filled the survey, they a multiple choice answer for ...
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1 vote
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### During Neural Network training, training loss decreases then hits an inflection point and increases. What are some possible explanations?

"During Neural Network training, training loss decreases then hits an inflection point and increases. What are some possible explanations?" I got this question in an interview and wondered ...
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