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.

learn more… | top users | synonyms

0
votes
1answer
590 views

Hypergeometric Distribution Problem With Rocks!

The question I am working on is: A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the ...
1
vote
0answers
78 views

How to determine the degrees of freedom of an inner-product matrix of two random matrices?

I have two random matrices A and B, with N columns each. The columns of A and B are independent but not necessarily identically distributed. A and B may be considered as two instances of an underlying ...
2
votes
1answer
4k views

Whats the difference between a one way anova and two way anova?

I know that in one way anova you compare the difference between two or more means and the same in two way, but I'm unclear as to how the use of categorical variables differs between them. Any help ...
-1
votes
1answer
117 views

Estimating component variance for a sum of random variables

Say I have two zero mean single variate independent random variables $X$ and $Y$, and a third variable $Z = X + Y$. I can draw samples $z_i$ with $i = 1..n$ from $Z$ and I know $Var(Y)$. How can I ...
0
votes
1answer
129 views

Help with Probability distributions

You are conducting a study of the relationship between the amount of rain in a field and the total mass of fruit produced by tomato plants. You randomly select tomato plants from a field and weigh ...
0
votes
1answer
4k views

Guessing number between 1-100 always can always be guessed in 7 guess. Why?

I'm no good at probability and statistics as this question will soon demonstrate. My question is this, I have an instructor who proved that he could guess a number between 1-100 using the divide and ...
0
votes
0answers
66 views

Probability/Statistics: $ Z $- or $ T $-test?

You have sampled the lengths of bird beaks from $ 50 $ birds, and the mean beak length is $ 10 ~ \text{mm} $ with a variance of $ 3 ~ \text{mm}^{2} $. What is the probability that the $ ...
2
votes
1answer
683 views

unbiased estimator of sample variance using two samples

I have a couple questions, I'm hoping someone can help! Let $X_1...X_n$ is a random i.i.d. sample from a $N(\mu,\sigma^2)$ distribution, and $Y_1...Y_m$ is a random i.i.d. sample from a ...
1
vote
1answer
157 views

I wonder if somebody could help me with this statistics probability problem?

I wonder if somebody could help me with this probability problem? You are collecting data on the success of a new anti-malarial drug on the incidence of malaria. You compare two samples: a treatment ...
1
vote
2answers
268 views

Cheese, mouse and a cat

I have a problem and I don't know how to solve it because I don't know where to start. If we have the following situation: Room 1-Room 2-Room 3-Room 4-Room 5 There is a little mouse in room 4 and ...
2
votes
1answer
39 views

How to determine the odds of a matching pattern where any single bit can vary

Let's say I have a data stream of bits in which I'm attempting to detect a sixteen bit sync pattern (The pattern is FB28 or 1111 1011 0010 1000 in binary, if that matters) If I allow a one bit error ...
1
vote
1answer
4k views

Finding the Derivative of an Expected Value.

Is it possible to find the derivative of an expression inside the expectation operator $ \mathbb{E}[\cdot] $? I have an expression that reads $$ \mathbb{E} \left[ \left[ \log(A_{k}) - ...
2
votes
2answers
861 views

Basic terms for the elements of an observation, sample?

I'm trying to write a database schema for measurements in a variety of categories, and am having trouble coming up with names for some basic elements. Let's assume we are gathering heart rate and ...
1
vote
0answers
181 views

cadf vs adf on residuals

I was wondering how I could interpret the results from the Spatial Econometric library's cadf and adf. Running cadf(TS1,TS2,0,1), I obtain the following: ...
1
vote
3answers
219 views

What is the $\operatorname{cov}(X, \max(X,Y))$ and $\operatorname{cov}(X, \min(X,Y))$ where $X,Y \sim N(0,1)$?

having trouble with this one. The exact questions is the $\operatorname{cov}(X, \max(X,Y))$ and $\operatorname{cov}(X, \min(X,Y))$ where $X,Y \sim N(0,1)$. i think the way to calculate it is to get ...
1
vote
3answers
175 views

Statistics - Cumulative Distribution Function

$$\begin{equation}F(x)=\begin{cases}0 &\quad x<-10 \\ 0.25 & \quad -10\leqslant x <30 \\ 0.75 &\quad 30 \leqslant x <50 \\ 1 &\quad 50 \leqslant x ...
1
vote
0answers
77 views

How to measure the streakedness of numerical data?

Would anyone know how to use C/C++ to calculate the streakedness of data? The definition of streakedness is how many deviations away from the mean(i.e running average a numerical data streak. Thank ...
-2
votes
4answers
3k views

Find the expected value of $\frac{1}{X+1}$ where $X$ is binomial

The problem: X is a binomial random variable, find $E[\frac{1}{X+1}]$ n and p are not given PDF for a binomial distribution is $\binom{n}{k}p^k(1-p)^{n-k}$ Expected value is $\sum{x_ip(x_i)}$ But ...
1
vote
1answer
131 views

Help with understanding the $\chi^2$-distribution

I'm studying statistics and there's one part in my book I can't understand. I tried to make as good translation as I can of the problematic part...here goes: Chi squared $\chi^2$ distribution Let ...
1
vote
2answers
107 views

Calculate a CDF given two PDFs.

I have two PDF's, $f_1(x)$ and $f_2(x)$ and I need to find the CDF (not PDF) of $f_3(x)$ where $f_3(x) = \frac{1}{2} (f_1(x) + f_2(x))$ I have already calculated $F_1$ and $ F_2$, the CDF's of ...
1
vote
2answers
193 views

Does “Cook's distance” tell us the outlier?

How many way to find the outlier? For cook's distance, which level is the cut off of outlier?
1
vote
0answers
109 views

Halloween candies!

Children go trick-or-treating in three mathematicians' apartments. In MathA's apartment, a child will roll a die and the number of candies the child receives will be the same as the outcome of the ...
1
vote
0answers
84 views

Theoretical justification for Cochran's rule in the $\chi^2$ test

There is an empirical rule performing a $\chi^2$ test for goodness of fit: the expected frequencies have all to be greater then or equal to 5. Does someone knows why? Is there any proof?
3
votes
0answers
102 views

Who established the word “ Degree of freedom ” in statistics?

I wonder who is the first one that established and applied the word : "degree of freedom" in statistics? Why he/she need degree of freedom in the calculation of many statistical values?
1
vote
1answer
286 views

Halloween candy picking probability!

Two persons, A and B are each picking up one piece of candy from a basket consisting 100 Kit-Kats, 200 Almond Joys, 300 Whoppers and 400 Skittles. A likes Skittles; B likes Almond Joys. What is the ...
2
votes
1answer
100 views

limit of an integral of a copula density function

let's say I have a copula density function which I denote as $c(x,y)$. $X$ and $Y$ are uniformly distributed RVs. I am curious if the following limit exists: $\lim_{u\rightarrow 1^{-}} \int_0^u ...
1
vote
2answers
334 views

Calculating Probabilities of a Random Variable Function

The problem is: A mail-order computer business has six telephone lines. Let $X$ denote the number of lines in use at a specified time. Suppose the pmf of $X$ is as given in the accompanying ...
1
vote
1answer
228 views

trying to verify pdf for distance between normally distributed points

Math people: I am trying to find the probability density function for the distance between two points in $\mathbb{R}^3$ selected independently according to the Gaussian pdf $F(\mathbf{z}) = ...
1
vote
1answer
527 views

Sufficiency and UMVUE for Poisson distribution

I need to show that $\hat\lambda = \bar X$ is a sufficient estimator for a Poisson distribution iid $X_1...X_n$, show that $\hat\lambda$ is the UMVUE for $\lambda$ and that $\hat\lambda$ is a ...
1
vote
2answers
2k views

How do you calculate IQR (interquartile range)?

I have the following data (ordered): $$0, 1, 1, 2, 3, 4, 4, 7, 9, 23.$$ As far as I know, $Q_1 \text{(median of the upper half)} = 1$; $Q_3 \text{(median of the lower half)} = 7$; Therefore, ...
3
votes
1answer
88 views

Can someone help me with this formula?

I'm writing a software algorithm at the moment which compares survey answers. Questions have $5$ possible answers, and a respondent could choose between 1 and 5 answers. What I'd like to do, for ...
1
vote
1answer
163 views

Bandwidth selection for kernel density estimation, using a Weibull kernel

Let $\{s_1,\ldots,s_N\}$ be a collection of N samples. I have performed the kernel density estimation using the classical form: $$ \hat{f}(x) = \frac{1}{Nh}\sum_{i=1}^N K\left(\frac{x-s_i}{h}\right) ...
2
votes
1answer
133 views

Zipfs law and LogNormal distributions

If a particular dataset has a lognormal distribution, will it also follow Zipf's law when the items are ranked? That is, say I have a set of populations of a random sampling of cities (assumed to be ...
2
votes
2answers
1k views

Show that $\hat\theta=\frac{2 \bar Y- 1}{1- \bar Y}$ is a consistent estimator for $\theta$

Let $Y_1,Y_2,...,Y_n$ denote a random sample from the probability density function $$f(y| \theta)= \begin{cases} ( \theta +1)y^{ \theta}, & 0 < y<1 , \theta> -1 \\ 0, & ...
0
votes
1answer
47 views

What is a “recurrent model” in forecasting

In this book, there is a chapter titled Recurrent Models (you can see that chapter in Google books) but it's very short and some parts are not very clear to me. Recurrent Models seem to refer to a ...
0
votes
1answer
65 views

Weights of airplane passengers

Due to rise in average Americans' weight guidelines are provided for airlines, expecting that plane passengers in the coming season will have an average weight of 190 pounds (luggage and clothes, etc, ...
1
vote
1answer
39 views

Alignment algorithm

So I'm trying to figure out to calculate some sort of alignment of strength score for a group of people's selections on various values. In this case, there are 36 values, each person selects gives 9 ...
1
vote
2answers
770 views

Symbols and naming in confidence interval

Suppose to have a confidence interval for the mean on a large sample, i.e. $$\overline{X}-z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}} \le \mu \le ...
0
votes
3answers
331 views

Finding the pdf of $Z=XY$, where the joint pdf of $(X,Y)$ is known

I've been trying to figure this out for a while. Suppose $X$ and $Y$ are random variables with joint pdf (probability density function) $$ f(x,y) = \frac{x+y}{15}, \quad\text{for }x = 0,1,2,\;\text{ ...
4
votes
2answers
2k views

Finding the MVUE using Rao-Blackwell Theorem

The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean $\lambda$. The daily cost of repairing these break downs is given by $C=3Y^2$ If $Y_1, Y_2, ..., Y_n$ ...
0
votes
1answer
83 views

Binomial distribution probability

A married couple decided to have $5$ children. Based on gene history, probability that any one of their children will need to wear eye glasses, independent of sex, is $60$%; probability that a child ...
2
votes
1answer
42 views

Bootstrap-related issue

Say I re-sample $N$ items with replacement from a numbered item sample of size $N$. What is the average number of data items that are not selected in each such sampling?
1
vote
1answer
68 views

AP statistics question

A bag contains 2 black and 2 white marbles, and there is a supply of extra marbles of each color. A move consists of randomly drawing 2 marbles from the bag. If the marbles are the same color, they ...
1
vote
1answer
381 views

How would you approach this problem on the Bayes theorem?

I've been reading a book on Statistics and I could COMPLETELY understand all of its text. It basically explained the bayes theorem and what priors were, what posteriors were etc. But then in the ...
1
vote
1answer
47 views

Clarification about Stochastic distribution

What does this mean - "the x distribution is stochastically smaller than the y distribution"?
1
vote
0answers
215 views

Formula for confidence interval in multi-variable regression

What is the formula for calculating the confidence interval for the expected value of $\hat{y}$ in a multi-variable regression model. In other words, I'm looking for the following formula just for ...
1
vote
1answer
309 views

Binomial Distribution Parameter & Probability

A married couple decided to have $5$ children. Based on gene history, probability that any one of their children will need to wear eye glasses, independent of sex, is $60$%; probability that a child ...
0
votes
1answer
205 views

Showing a moving average is strictly stationary if underlying sequence is strictly stationary.

Just as the title suggests, this is my problem: Let $Z_t$ be a strictly stationary sequence. Define $X_t = Z_t + \theta Z_{t-1}$. Show that this sequence is also strictly stationary. Here's my ...
0
votes
1answer
449 views

Normalizing a normally distributed vector to unit length

If I have a random vector $\mathbf{y}$ generated from multivariate gaussian distribution $\mathcal{N}(\mathbf{0}, \mathbf{C})$, then I normalized it to unit length, which is, $$\mathbf{y} \sim ...
5
votes
5answers
9k views

Given a data set, how do you do a sinusoidal regression on paper? What are the equations, algorithms?

Most regressions are easy. Trivial once you know how to do it. Most of them involve substitutions which transform the data into a linear regression. But I have yet to figure out how to do a ...