# Tagged Questions

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

36 views

### Check for Independence

Given $$f_{(U_1,U_2)}(u_1,u_2)=\begin{cases} 1/2& -u_1<u_2<u_1 \text{ and } u_1 - 2 < u_2 < 2 - u_1 \text{ and } 0 < u_1 <2\\ 0& \text{otherwise}\end{cases}$$ I found that ...
76 views

### What's the “ridge” in Ridge Regression?

In normal least squares, we try to find $\hat\beta$ which minimizes $$\|y-X\beta\|^2$$ Ridge regression expands this to "penalize" certain values of $\beta$ via a matrix $\Gamma$: ...
145 views

Suppose that I have N different businesses running during the summer. Let us further suppose that I estimate (using regression) the income for each business with a 95% confidence interval. I then sum ...
75 views

534 views

137 views

### MLE of uniform distribution

Now before I begin, I know this question has been asked multiple times but all the answers but I had so many questions of my own that I figured I should make a new question as my thoughts are ...
7k views

### In how many ways can 20 identical balls be distributed into 4 distinct boxes subject?

I was practicing math exercises on text book and i got stuck in this question ? ...
91 views

### Testing hypothesis - type I and type II error

I have given following information: $n=15$ - sample size $S_n=0.013$ - sample standard deviation I have to test null hypothesis $H_0(\sigma=0.01)$ agaist alternative hypothesis ...
111 views

### Introductory Statistics/Probability Reference Request

I am a PhD student in mathematics with a background in Pure Mathematics. As such I have pretty much zero background in statistics or anything other than the most basic probability (i.e., what one ...
54 views

### Which probability in this hypothesis test?

We have a hypothesis A (null hypothesis) such that $p\le 0.6$ and B such that $p>0.6$. Now we want to develop a deterministic test $\phi$ for 20 people that has a safety of 95%. Hence we would be ...
172 views

### Statistics - Lost with this question

I'm having trouble doing this question because I don't know where to begin. Could someone walk me through this slowly so that I understand the thought process and how to approach questions like this? ...
2k views

### PCA using SVD in Matlab, a few questions.

I have X = [25, 2000] i.e. 25 subjects and 2000 values (i.e. each subject has a spectrogram that is reduced to 2000 values). My goal is to reduce from 25 subjects to 1 or 2 "subjects" that best ...
21 views

### Does the order of samples taken affect the probability of getting a certain value?

The question is asking what is the probability of taking two samples and having the first one being shorter than 20 and the second one being larger than 25 based on the given density curve The ...
55 views

### Convergence rate of an estimator

Say we are interested in estimating some unknown real scalar parameter $\alpha$ using data. Suppose the estimator $\widehat \alpha_N$ of $\alpha$ using the data is consistent. I want to know what it ...
57 views

### Why is the marginalized inverse-Wishart distribution not equal to the inverse-gamma distribution?

Given that the inverse-gamma distribution is the one-dimensional version of the inverse-Wishart distribution, why will (philosophically speaking) an inverse-Wishart distribution that originally has ...
58 views

18 views

### How do I design a reward function given two parameters

We want to design a reward function R(x, y) where $x \in [0, 1]$ and $y \in (0, 10000)$ such that x is the dominant term when its value is close to or equal to 1, whereas y is dominant when x is ...
42 views

### Linear Regression Question (Linear Algebra) Help!!

Hey guys, I have a quick question. I am trying to prove that the squared sample correlation between fitted and observed values is equal to $R^2$ (coefficient of determination). I am having a lot of ...