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

-1
votes
1answer
41 views

Books on Statistics and Optimization

I'm trying to close gaps in my education especially in Statistics and Optimization theory. I had an awful class on Statistics so I want to learn it by myself. As for Optimization we had a pretty good ...
0
votes
2answers
34 views

Distinguishing between unimodal and bimodal normal data

I have a large number of data sets that have either a unimodal normal distribution or a bimodal normal distribution. I'm not a statistician by any means, so I'm quite limited in my experience. For ...
1
vote
1answer
20 views

t distribution : formula for the degrees of freedom

I understood why we are using a t distribution in this case , because the sample isn't big enough to approximate the true standard deviation of the population by the sample's . But what I can't find ...
0
votes
1answer
13 views

Continuously go from a lognormal distribution to a power law

Do you know any phenomena that are described by a continuous mappings between a lognormal and a power law distribution? Of course, one could give a simple linear combination of the two ...
1
vote
0answers
23 views

What should I be studying if I want to calculate correlation between data sets?

I'm building an app that brings in data from multiple API's (Stripe, Google Analytics, Github). I'd want to be able to analyze the different sets of data against each other if at all possible and draw ...
1
vote
1answer
54 views

A Game of Coin and Die

This game is played with a fair coin and a die. First player flips a coin. If it turns out head(H), the player proceeds with tossing a die. If it turns out tail(T), the player proceeds with flipping a ...
2
votes
1answer
23 views

Properties of the solution of a linear system with random equations

$x_i$ is drawn from $\mathrm{unif}(a,b)$, $y_i$ is drawn from $\mathrm{unif}(c,d)$. $x_i$ are independent from each other. $y_i$ are independent from each other. $x_i$ are independent of $y_i$. $i$ ...
0
votes
2answers
35 views

How to compute approximate probability with z value?

This is the question: An airplane with room for 100 passengers has a total baggage limit of 6000 lb. Suppose that the total weight of the baggage checked by an individual passenger is a random ...
0
votes
0answers
25 views

How can I calculate definite integral of chi-squared pdf with one degree of freedom

enter image description here I need a calculating process of the above definite integral please help me.. (sorry for my poor English)
1
vote
2answers
16 views

Is this altered formula for correlation still bounded by $-1$ and $1$?

Recall that $$ ‐1 \le \text{corr}(X,Y) = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \le 1 $$ The proof for this bound uses the Cauchy Schwarz inequality, and I've been trying to wrap my head around ...
-1
votes
0answers
31 views

How to find P(Y≥k) for a Poisson distribution

The original question is P(Y=y) for k-1≥y≥0 and P(Y≥k) for x=k. And find the expected value for Y. I know that the expected value of Y is the sum of two separate parts, which is the summation of ...
0
votes
0answers
19 views

deriving the profit function given probability distributions

I can't seem to get much further in deriving the profit function for part (c). I've attached the question and my attempt, but I'm not sure on what to do next, or if I've done something completely ...
0
votes
3answers
33 views

Is it true that $\frac{E[(|X - E[X]|)(|Y - E[Y]|)]}{\sigma_X \sigma_Y} = 1$?

Consider the well-known fact that correlation is bounded between $-1$ and $1$: $$ -1 \le \text{corr}(X,Y) = \frac{E[(X - E[X])(Y - E[Y])]}{\sigma_X \sigma_Y} \le 1. $$ I've been trying to wrap my ...
0
votes
0answers
32 views

Odditiies in a StackExchange reputation distribution

As we know from for eg M.SE reputation distribution the reputation distribution is a neat power function, that's to be expected. However, on Travel StackExchange (possibly elsewhere, didn't research ...
2
votes
0answers
51 views

How to use Expectation Maximization (EM) in Item Response Theory (IRT)?

Could you give a worked example on the steps of Expectation Maximization in Item Response Theory if we use the Two Parameter Rasch Model. The student abilities are unknown and the question parameters ...
2
votes
2answers
40 views

Is covariance preserved under transformation?

Let $X_1,X_2$ be normally distributed random variables with $\rho = 0.5$, mean equal to $0$ and variance equal to $1$. Let $U_i = \Phi(X_i)$ where $\Phi$ is the marginal distribution of $X_1,X_2$. We ...
0
votes
1answer
18 views

Calculate confidence interval when only given alpha?

Is there a formula to properly calculate the confidence interval when you're only given alpha and sample data? Thanks!
0
votes
1answer
28 views

Computing the “Mean Value” of a Point Sample From an Arbitrary Manifold

A friend of mine noticed that taking the "mean" of two points on the circle isn't as easy as just computing the arithmetic mean of their arguments: If one point has argument $-3.13$ radians and one ...
0
votes
1answer
46 views

Calculating the covariance matrix

I'm working through exercises in my textbook and I'm stuck on calculating the covariance matrix. We are given a random vector $$X = \pmatrix{X_1\cr X_2\cr}$$ with expected value $$\mu = ...
0
votes
0answers
26 views

Is simple statistical analysis of correlational data for the purposes of prediction practiced? Is it recommended? [migrated]

I want to implement a facility in my web-app which marks user contributions that, relative to the contributions which respectively precede them, have a high likelihood of being acts of vandalism. The ...
0
votes
0answers
17 views

Bounding the $q$-th moment of a Gaussian random variable

I have come across an inequality which confuses me: Suppose $X$ has a Normal$(0,\sigma^2)$ distribution. Then $$ (\mathbb{E}|X|^q)^{1/q} \leq \text{const.} \sqrt{q} \sigma $$ for $q\geq 1$. I ...
0
votes
0answers
6 views

Error ellipsoid for Gaussian covariance matrix?

When we are given a Gaussian covariance matrix, it is said that by some eigenvalue decomposition, we could plot an ellipsoid to visualize this covariance. But I am not sure how to do it in detail ? ...
0
votes
0answers
33 views

Estimating distribution from two distributions

I have been doing a survey on Family Incomes in India. The income of male and females are denoted by x and y. x and y are strictly positive. Per chance, individual values of y were deleted. I only ...
5
votes
2answers
59 views

In layman's terms what is the difference between a model and a distribution?

The answers (definitions) defined on Wikipedia are arguably a bit cryptic to those unfamiliar with higher mathematics/statistics. I am a high school student very interested in this field as a hobby ...
1
vote
1answer
25 views

Likelihood ratio test proof

I'm trying to understand a proof given by my statistics textbook. It's a proof presented in relation to the likelihood ratio test. $$\sum_{i=1}^n (x_i- \mu_0)^2 = \sum^n_{i=1}(x_i-\bar x)^2+n(\bar ...
-1
votes
1answer
26 views

Independent and identically distributed question (Please help check the answer)

Please help me check my answer. The question is: My calculation I think it's quite simple that's why I'm not too sure. I used the theorem $E(X_1 + X_2+X_3+... +X_n) = E(X_1) + E(X_2) + E(X_3) + ...
2
votes
1answer
19 views

Why prefer the t-score when the sample size is low?

According to this link: The general rule of thumb for when to use a t score is when your sample size meets the following two requirements: The sample size is below 30 The population ...
0
votes
1answer
12 views

Estimator defined as sum of random variables and confidence interval

I'm trying to solve a problem and I'm stumped. Let the continuous random variables $X_1$, $X_2$, $X_3$ and $X_4$ be independent such that $X_1 \sim N(\mu, 1^2)$, $X_2 \sim N(\mu, 2^2)$, $X_3 \sim ...
0
votes
0answers
40 views

If this mean time is estimated to be in excess of 7 days, a new process will be implemented to reduce production costs.

a) You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the mean time ...
0
votes
0answers
17 views

The prime minister will accept an error of $5 million in the estimate of µ.

Government officials in Canberra have recently expressed concern regarding overruns on military contracts. These unplanned expenditures have been costing Australians millions of dollars every year. ...
-1
votes
1answer
22 views

A Basic Question E-views

I ask a question about E-views. Is the P-value in the picture less than 0.05 or greater than 0.05? I'm confused because of the presence of the sign '<' in front of 0.10. Please help mee. Thank you. ...
0
votes
1answer
22 views

How is the t-statistic computed in this context?

According to pg. 55 of Statistics in Plain English, the t-statistic for the sample mean is $$ t = \frac{\bar{x} - \mu}{s} $$ where $\bar{X}$ is the sample mean, $\mu$ is the population mean, and $s$ ...
0
votes
2answers
14 views

Show that $\frac{\alpha+y}{\alpha+n+\beta}\in (\frac{\alpha}{\alpha+\beta};\frac{y}{n})$

Suppose you assign a $Beta(\alpha,\beta)$ prior distribution for $\theta$, and the you observed $y$ heads out of $n$ spins. Show algebraically that your posterior mean of $\theta$ always lies ...
0
votes
0answers
7 views

What is the minimal value of Cohen's kappa?

We are in the context of two classifiers, classifying $N \in \mathbb{N}$ datapoints into $z \in \mathbb{N}$ classes. Let $h_{ij}$ be the count of objects being classified to class $i$ by the first ...
1
vote
1answer
16 views

Why is the degrees of freedom for a matched pairs $t$-test the number of pairs minus 1?

Cross-posted at Stats SE. It is eligible for bounty in 12 hours, but before I put a bounty on it, I would like to ask it here. I am used to knowing "degrees of freedom" as $n - r$, where you have the ...
0
votes
1answer
29 views

Correlation and Linear Regression

I'm tasked with this question but unable to proceed on. Q: Calculate the linear product moment correlation coefficient between x and m for these samples: $$ \Sigma x=205,\\ \Sigma m=1240, \\ \Sigma ...
0
votes
0answers
16 views

Can distributions scale to any given time scale?

I am working with some colleagues to set up alerts based on call center data, and I feel that something is wrong with how it is currently being done, but I'm not sure what exactly, or how to explain ...
1
vote
1answer
66 views

Comprehensive conditional probability question

Bob owns a bakery. It is located on a busy road with a lots of individuals walking by the bakery each day. On average, $\lambda$ individuals go into the bakery per day, the number of individuals ...
1
vote
1answer
60 views

Finding the mean age of a wedding guest list

Earlier I asked this question. So, similarly, imagine the same type of list with elements having a guest and probability of attending, but now each guest also has an age. How can we calculate the ...
0
votes
2answers
31 views

Understanding independence. Sample space $S = \{1,2,3,\ldots,20\}$ and events $A_n = \{x \in S: x \: \text{is a multiple of} \:n\}$

The one in blue are the solution. $x$ is the multiple of $n$ which mean $A_2$ should equal to $4$ right? and $P(A_2)$ should equal to $1/5$ (As $2/20$). Why in the solution, $P(A_2) = 1/2$ ? ...
1
vote
1answer
20 views

how is chi square test interpreted for cross tables?

Stats newbiew here. I understand that I use the chi square test to be able to calculate the probability that an observed value is due to chance against an expected value. I understand that it can be ...
1
vote
2answers
30 views

Finding Type I error

Suppose the sample size $n=16$ is drawn from a normal distribution with mean $\mu$ and standard deviation $\sigma = 4$. Consider the testing hypothesis $H_o:\mu = 0$ vs $H_a:\mu \ne 0$. Let the ...
0
votes
0answers
7 views

Placing upper bound on an error rate. Contrasts. Stats.

I need some help understand what this actually is. My textbook asks a question but never discusses what placing an upper bound is. So a research study conducted an experiment with 5 treatments, four ...
0
votes
1answer
9 views

Calculating the ratio of services to total jobs installed in one year.

I have had a total of 69 jobs this year, 13 of my jobs have had services this year. What is the ratio of services to total jobs?
0
votes
0answers
6 views

How to determine the spectral distribution and its density for a stationary GARCH process?

I am having problems with determining the spectral distribution and its density for a stationary GARCH process. I have no idea what to do. I would appreciate some hints, not the solution but hints or ...
2
votes
1answer
19 views

Testing the Uniformly Most Powerful Test against the alternative

Hi I am working on the following problem A single observation $X$ is made from one of three densities listed below with parameter space $\Theta=\{0,1,2\}$. \begin{align*} ...
0
votes
0answers
21 views

How is this not a counter-example to the fact that the standard deviation of a standardized random variable must be 1?

Let $X$ be a random variable that sends all members of the sample space to some constant real number $c$. Let $Z$ be its standardized counter-part. The standard deviation of $X$ is $0$, since $X$ is ...
2
votes
1answer
19 views

Paired T-Tests vs Independent

The effectiveness of a training course is examined, and performance of each individual in a group is taken both before and after, and the differences are used in a paired T test. Would it be possible ...
0
votes
1answer
15 views

Weighted Average or Non-Weighted Average for this?

I surveyed people for a thesis I made, and want to calculate the standard deviation of their results, however I am not sure whether or not I should use weighted average or non-weighted average, my ...
0
votes
0answers
8 views

Logistic regression probabilities

I have performed a logistic regression on some data, and the function is: $p(x,y) = \frac{\exp(4.5 + 3.5x - 0.1y)}{1+\exp(4.5 + 3.5x - 0.1y)}$ This also gives you the probability of observing some ...