# 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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### Small sample-size, two sample test, power calculation

We have two normally distributed random variables with means $\mu_X$ and $\mu_Y$. We test the null hypothesis $H_0:\mu_X-\mu_Y=\delta=0$, at significance level $\alpha$ in a two-tailed test. We sample ...
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### Invertibility of covariance matrix when number of training examples are lesser than number of features

I was trying to study an outlier detection algorithm and realized that in case we use a multinomial Gaussian distribution to model data then the invertibility of Covariance matrix ($\sum$) is ...
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### Could someone use this concrete data set to illustrate how to compute the average Gain?

Chapter 3, Page 86 of Tom M. Mitchell. Machine Learning (free) says One practical issue that arises in using GainRatio in place of Gain to select attributes is that the denominator can be zero or ...
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### Determine if the following Markov chain is positive recurrent, null recurrent or transcient

We consider the Markov Chain with transition probabilities $$p(i,0)=\frac{1}{i^2 +2},\qquad p(i,i+1)= \frac{i^2 +1}{i^2 +2}.$$ Determine if this Markov chain is positive recurrent, null recurrent ...
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### How to find a percentage change with multiple percentage rates? [closed]

If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be effect on its area? A. 16% decrease B. 8% decrease C. No change D. 16% increase E. 8% increase
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### What is the rejection region for this test?

A sample of size 16 was randomly drawn from a normal population with known standard deviation σ = 5. The sample mean is equal to 20.5. The researcher wants to run the followingz-test(α=5%): H0 :μ=...
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### Show regression line passes through points $(X_1,\bar{Y_2}),(X_2,\bar{Y_2})$

Assuming a simple linear regression model , $n_1$ points are sampled at $X_1$ and $n_2$ at $X_2$ and let $\bar{Y_1} , \bar{Y_2}$ be the averages at $X_1 , X_2$ respectively. The problem that I am ...
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### Introduction to Statistical Learning

For those that have read the book Introduction to Statistical Learning, I'm having a problem understanding a certain line: I can't seem to understand the derivation from the first equality to the ...
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### How can I find the marginal distributions of $\frac{X_1}{X_1+X_2}$ and $\frac{X_2}{X_1+X_2}$? [duplicate]

Let $X_1 \sim Gamma(\alpha_1,1)$ and $X_2 \sim Gamma(\alpha_2,1)$ be independent random variables. How can I find the marginal distributions of $\frac{X_1}{X_1+X_2}$ and $\frac{X_2}{X_1+X_2}$? By ...
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### Expected wait time in two different types of banks?

Problem Statement There are two banks both have 100 people inside who want to cash their check and must do so by talking to the teller. In both banks, there are 10 tellers. In Bank 1 all 100 people ...
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### linear dependence and 0/1 features in ML

This question is in the context of machine learning. I don't know much statistics (I'm just a software engineer who finds machine learning cool), and I was confused by something I just read in a book. ...
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### Relationship between repeated measures ANOVA and random / mixed effect models

This is not concrete question but more a conceptual one, although a pretty low-level one I guess: When I was taught ANOVAs the 'classical' sums of squares way, I was told that repeated measures can ...
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### Testing of Hypothesis using Anova

Let $y_1=\alpha_1+e_1,y_2=2\alpha_1-\alpha_2+e_2$ and $y_3=\alpha_1+2\alpha_2+e_3$ where $e_i \sim N(0,\sigma^2)$ iid for $i=1,2,3$. Find the least square estimate of $\alpha_1$ and $\alpha_2$. Derive ...
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### Poisson Distribution vs Binomial Distribution

I have a specific problem here. It is stated as: "Assume that 30% of students in a university take public transportation daily to commute to their college. Suppose 10 of the students are randomly ...
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### Why autocovariance is 0?

First of all I am a newbie in stats, trying to study statistics, and somehow I find 'time series' way more difficult than other topics. I am confused with the “autocovariance”. In the book "Time ...
If $X_1 , X_2 , ... X_n$ are iid and they have the same pdf $f_θ(x)$ . Consider testing $H_0 : θ= θ_0$ vs $H_n : θ = θ_0 +Δ * n^{-1/2}$. where , $Δ = (Δ_1 , Δ_2 , .. Δ_k)^T$ We want to find the ...