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
0answers
10 views

Maximum density linear combination chi squares

I have a positive linear combination of chi square variables \begin{equation*} X=\sum_{i=1}^k \lambda_i \chi^2(r_i), \end{equation*} the degrees of freedom satisfy $r_i>1$. I need an upperbound ...
-1
votes
0answers
7 views

Confidence interval of exponential random variables

I have a sequence of random variables $X_1, X_2, ..., X_n$ such that $X_i = e^{-(x_i-Θ)}$ I have to construct a confidence interval of the form $[Θ−c,Θ]$,where $Θ = \min _i{X_i}$. For $n = 10$ how ...
1
vote
1answer
28 views

Confidence Interval for Pareto Distribution

A random variable is said to have probability density function $$f_X(x)=\frac{\alpha k^\alpha}{x^{\alpha +1}},\quad \alpha , k>0 \; \text{ and }\; x>k.$$ 1. Compute the MLE estimators ...
2
votes
2answers
11 views

Finding the probability of time between two events for a poisson process

If two events occur at a rate of 1.8 per hour on average, and this occurrence follows a poisson process, what is the probability that there is at least 1 hour between two events? My approach for this ...
-3
votes
0answers
12 views

Stat MGF question [on hold]

Suppose we are given a random variable Y with probability density function f(x) = exp(((xƟ -b(Ɵ))/Φ) + c(y,Φ)) show that the moment generating function is: exp((b(Ɵ+Φt) -b(Ɵ))/Φ) Any ideas on how ...
1
vote
1answer
27 views

Is there a method to check if two curves (non-linear) are identical

I have two data sets of pollutant concentration on simultaneous days. I have to check whether these two curves follow similar pattern or not ( there might be some time lag between both) on daily ...
0
votes
0answers
22 views

Skellam CDF Increasing vs Decreasing in a parameter

I'm working with the following Poisson difference distribution: $$\text{Prob}\{X_1-X_2 \geq 0\} $$ where $X_1 \sim$ Poisson $(\mu_1)$ is independent from $X_2 \sim$ Poisson $(\mu_2)$. I need to ...
-3
votes
1answer
132 views

Why should statistics be considered mathematics? [on hold]

Statistics should be completely separate from mathematics because it is not exact as pure mathematics , so my question is why they are still together? Statistics is a science in my opinion, and it is ...
2
votes
1answer
21 views

Confusion about the sample mean and random variables

As I understand the sample mean you just add a bunch of random variables that constitute a sample from their common distribution and divide by the number of those same random variables. When I apply ...
1
vote
1answer
26 views

What does “2- place real function” mean?

What does "2-place real function" mean? This comes up in the context of copulas, as here.
1
vote
0answers
20 views

Estimating the size of my population

I have a following problem: Imagine you have a hat with many different balls in it and you want to estimate, how many balls are totally in the hat. The only think you are allowed to do is to take one ...
-1
votes
0answers
105 views

Pareto distribution,fisher information, confidence interval

Having a bit of problem at these questions, greatly appreciated if anyone can solve them. For the notation, k^ is k with a hat on top of it, don't know how to do that on a keyboard. The rest is ...
1
vote
0answers
36 views

Density functions and estimators

A random variable is said to have probability density function $$f_X(x)=\frac{\alpha k^\alpha}{x^{\alpha +1}},\quad \alpha , k>0 \; \text{ and }\; x>k.$$ 1. Compute the MLE estimators ...
2
votes
1answer
25 views

Confidence Interval Question - Confused on Approaching the Problem

My question is almost exactly the same as another one here on math stack exchange, but it isn't as explanatory as I'd like it to be with some parts. I was unsure of whether or not it'd be "okay" to ...
2
votes
1answer
26 views

Probability of co-occurence

Of total $N$ people, $m$ people are good at mathematics and $c$ people are good at computer science. What is the expected number of people good at both mathematics and computer science? Or what is the ...
0
votes
1answer
23 views

proof of the convergence of confidence intervals

The confidence interval can be derived intuitively by replacing the standardized mean with the standard normal and variance with sample variance, but is there a formal limit? I'm trying to prove if ...
1
vote
1answer
46 views

Fisher information matrix of MLE's

I know what it means to compute the fisher information matrix of a vector of parameters. However, how does one compute the fisher information matrix of a vector of MLE's? Specifically, I am working ...
0
votes
0answers
11 views

finding min and max after removing percentage of num values knowing the standard deviation.

I have a question i have some data and i know it's (number of values, min, max, mean and standard deviation) can I know the minimum after removing x% of the total number of values and the maximum ...
0
votes
0answers
14 views

I would like to know how to do log transformation of hyperparameters in Gaussian Process Classification.

I am using Gaussian Process classification and I want to do log transform of the hyperparameters so that they are all positive. From this www.lce.hut.fi/research/mm/gpstuff/GPstuffDoc.pdf document, I ...
0
votes
1answer
28 views

Which statistics test to be used? [on hold]

I want to run a statistics test in SPSS that tests the potential differences in two sets of data. The first set contains the following ten values: 13.7, 34.0, -68.0, 19.8, 20.9, 23.1, 22.5, 18.4, ...
-1
votes
0answers
26 views

Prooving a sequence of iid within an interval

How would I solve part 3 given that I have done the previous questions?
1
vote
2answers
287 views

Average distance between two randomly chosen points in unit square (without calculus)

Imagine that you choose two random points within a 1 by 1 square. What is the average distance between those two points? Using a random number generator, I'm getting a value of ~0.521402... can ...
3
votes
1answer
41 views

How to prove the sign test

Please correct me if I'm wrong, but a version of the sign test assumes under $H_0$ that there is some distribution $F$ where $X_i \sim F, Y_i \sim F$ and $X_i, Y_i$ are iid. Then it states that $T = ...
0
votes
3answers
36 views

Probability of a Rare Event Occurring within a Certain Number of Times

I'd like to know how to find the probability of an event occurring, given the probability of that event, within a certain number of chances for it to occur. For example, say that once every year ...
1
vote
1answer
79 views

How to minimize the expectation?

Given random variables $X_0, X_1, \ldots, X_n$ with finite expectations $m_0, m_1, \ldots, m_n$ I want to prove that the numbers $a_i = \frac{\det \Lambda_{i0}}{{\det \Lambda_{00}}}$ minimise the ...
-2
votes
1answer
21 views

statistics testing a claim please help. homework problem and stuck [on hold]

Systolic blood pressure levels for men have a variance of 388.09 mm^2 HG. a random sample of 31 women resulted in blood pressure with a variance of 497.29 mm^2Hg. Use a 0.05 significance level to test ...
1
vote
0answers
15 views

Confidence interval from covariance matrix

We have a matrix of stochastic variables $X\sim\mathcal{N}(0,\Sigma^2)$, where $\Sigma^2$ is a positive definite covariance matrix. How do we calculate the 95% confidence interval for X? (lets say ...
3
votes
1answer
14 views

Bivariate Normal Distribution Problem vs Marginals

If $X_1 \sim N(0,1)$ and $X_2 \sim N(X_1^2, 1)$ then does $(X_1, X_2)$ follow a bivariate normal distribution? My thinking is that $X_1 ^2$ is $\chi^2_1 $ since it's the square of a $N(0,1)$ random ...
0
votes
0answers
20 views

Combination of historical and current data in statistics

I have a general question about a statistical matter. Lets assume there exists a true and unique probability $p$ such that an event $X$ happens in the next 12 months. There is some information about ...
0
votes
0answers
29 views

Algebra Integral simplification

Let some equation problem final result is like this $0\leq1\leq s\leq t\leq u\leq v$ \begin{align} M=\mathrm{exp}\bigg\{-\pi\lambda v^2+\pi\lambda v^2\bigg(\displaystyle\int_o^s ...
1
vote
1answer
29 views

Standard deviation: calculating how polarizing a question is

I'm trying to calculate how polarizing a question is. Let's say I have a question that has 3 possible choices. A certain percentage of people choose a specific answer. Answer a: $30\%$ Answer b: ...
2
votes
3answers
38 views

2 restaurants located randomly

any help on following question will be much appreciated. Q. Suppose that $2$ restaurants are going to be located at a street that is $10$ km long. The location of each restaurant is chosen randomly. ...
2
votes
1answer
82 views
+50

Sum of i.i.d. random variables and finding an upper bound

Problem: Suppose that $(X_i)_{i\in\mathbb{N}^+}$ is a sequence of i.i.d. random variables. For some $n\in\mathbb{N}^+$, let $S_n=\sum_{i=1}^n X_i$. Furthermore, let $a$ be a positive constant, and ...
0
votes
1answer
28 views

Challenging probability and statistics problems?

The books I have on the subject lack entertaining problems. Can someone suggest a book with more challenging problems - perhaps not at olympiad level, but a bit easier. Thanks very much!
1
vote
0answers
25 views

Explanation of Cramer-Wold theorem

I was trying to understand mathematically what the statement of Cramer-Wold theorem means. Intuitively, I was told that two probability distribution $P,Q \in \mathbb{R}^n$ are equivalent if all their ...
0
votes
0answers
15 views

If the null hypothesis is true, how will the test statistic be distributed?

I went with T~(50-6) The question goes.... "A regression is estimated with 50 observations, five explanatory variables and with a constant. Suppose You want to test the following hypothesis $H_0: ...
0
votes
0answers
8 views

Confidence interval for mean using t-distribution (unknown pop.variance). Is the following statement true or false?

This is from an A-Level statistics paper. We are the given the lengths of 10 components and asked to calculate a 95% confidence interval for the mean. We are given that the lengths are normally ...
2
votes
3answers
44 views

Parameters estimation for gaussian function with offset

I've read the paper Least square fitting of a Gaussian function to a histogram by Leo Zhou on how to perform a Least Square Fitting of a gaussian function to a histogram. The Gaussian function used ...
1
vote
1answer
9 views

Topics under Model Based Cluster Analysis

Can anyone recommended topic(s) I could use for my thesis under "Model Based Cluster Analysis"? I initially used "Inference in Model Based Cluster Analysis" as my working topic but appears to be ...
0
votes
1answer
42 views

A CD players plays songs until a certain artist is selected.

Suppose you have a CD player with 10 CDs where 9 of those CDs belong to an artist A and 1 CD belongs to an artist B. Suppose this CD player will pick a CD at random, and from that CD it will pick ...
1
vote
1answer
19 views

goal programming, mixed-integer program, optimal compromise goals, statistics

QUESTION Can someone help me figuring out how to calculate this question? In this question, I have 4 variables (I think it would be more easily to calculate), and 5 goals. SO for the 27 boxes, I ...
0
votes
0answers
24 views

Maximizes the expected utility, Decisition making, statistics

QUESTION Can someone help me figuring out how to calculate this question, i just learned this stuff and i haven't do any example like this before... So i'm interpreted this question as: We need ...
1
vote
1answer
33 views

Testing randomness

I'm looking for informations about randomness and especially - random numbers. I found some about random number generators, but for now, the question, that concerns me is how statistically differ ...
0
votes
1answer
11 views

Maximization of a statistical property of a subset of random numbers

I have encountered a maximization problem which could be formulated as a discrete mathematics problem arising from statistics, but I don't know where to start or which techniques could be applied to ...
2
votes
1answer
27 views

Finding yearly weather statistics from tomorrow's weather probability

I'm trying to solve this problem from a book, but so far I haven't found how to approach it... I made a graph, and tried to calculate some probabilities.. but nothing What should I do? Thanks!
0
votes
2answers
17 views

What is a decision threshold and how does it apply to a statistical power?

I'm pretty confused on what is actually going on in this section with hypothesis testing. As another note, the values below are computed using R. I have a homework problem that says: From the ...
0
votes
1answer
27 views

Why is the Venn Diagram Considered a Special Case of the Formula for Unions

$P( A \cup B) = P(A) + P(B) - P(A \cap B)$ Or in Boolean terms: $P(A + B|C) = P(A|C) + P(B|C) - P(AB|C)$ I've read a lot of information but still can't piece together why this would be considered a ...
0
votes
1answer
29 views

Is the product of $n$ Normal distributions also a normal distribution? [on hold]

Is the product of $n$ Normal distributions also a normal distribution? I need not derivation just but answer.
0
votes
0answers
9 views

Consistent estimators/convergene in probability and slutsky

Let $m_n$ be a consistent estimator of $g(\vec\alpha)$ where $\vec\alpha = (\alpha_1,\cdots,\alpha_k)\in \mathbb{R}^k$ and $v_n$ be a consistent estimator of $f(\alpha_1,g(\vec\alpha))$. Suppose that ...
0
votes
1answer
15 views

calculating variance problem

When calculate variance, It's 1/2E((x-0.1)^2)+1/2E((x+0.1)^2)-E(x)^2 Is it right? So, the answer is 0.01 Am I missing something? And whenever I calculate the vatiance of the second estimator ...