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.

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Moving average where periods have unequal # of samples

I'm trying to compare a simple moving average approach to one that normalizes by the number of samples in a period to determine which is "more correct." Here's a representative piece of the data: ...
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1answer
17 views

Computing the Density of Points on a 2D Plane

I have a chart with points scattered across it; many of which are tightly clustered. I wish to filter out all points that are not within these dense clusters of points. I have an idea of how to ...
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1answer
15 views

Difference between stochastic process and chaotic system

Can anyone please point out some difference and similarity between stochastic system and chaotic system?
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1answer
16 views

How do you manage fractional counts in a binomial calculation?

How do you choose the counts to include in a binomial calculation if the range of counts is not discrete? For instance, given a binomial distribution of 110 counts and a probability of 0.301 of ...
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1answer
34 views

Statistics - normal distribution problem

Two random variables $X$ and $Y$ are i.i.d. normal$(\mu, \sigma^2)$. If $P(X > 3) = 0.8413$ find $P((X+Y)/2 > 3)$. The result must be exact number, so normal distribution parameters are ...
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0answers
18 views

Probability of selecting a sequence in order

If "X" number of attempts are made by "Z" number of persons to select a random number from a range "r", where "X <= r". Then I am interested in finding the probability that a particular sequence in ...
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1answer
26 views

Is the mode of the sum the same as the sum of the modes

If we have $N$ sets, $\{A_{1},\dots, A_{N}\}$, and we form a set $S$ by taking the sum of each element in the set with each element in the other sets, what can we say about the mode of $S$? ...
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1answer
53 views

Why does this expectation integrate to 1

Let $p(y|\theta )$ be our likelihood, and $p_{N}(\hat{y}|\theta)$ be an unbiased estimator of our likelihood. Let $z=\ln p_{N}(\hat{y}|\theta) - \ln p(y|\theta )$, and $g_{N}(z|\theta)$ be the ...
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1answer
32 views

the probability density function (PDF) of concatenation of two Gaussian variables

Gaussian variable $x$ follows from $N(u_x,\sigma_x^2)$ and $y$ follows from $N(u_y,\sigma_y^2)$. Assume we have the vector $\bf{z}=[x,y]^T\in R^2$, then it seems that no matter whether $x$ and $y$ are ...
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1answer
19 views

Two types of errors, type-$1$ error and type-$2$ error, can not be minimized simultaneously when the sample size $n$ is already fixed. How?

I read in some of the books that the two types of errors, type-$1$ error and type-$2$ error, can not be minimized simultaneously in Neyman Pearson Theory of testing of hypothesis when the sample size ...
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2answers
38 views

Erin rolls 4 four-sided dice all at once, then can roll a subset of her choosing a 2nd time. What is the probability of getting all the same number?

Here's what I have so far: All 4 same on first try = (1/4)^4 * 4 3 same, then get 4th on 2nd roll = 4 * (1/4)^3 * (3/4) * (4!/3!) Here's where I'm confused: 2 same = 4 * (1/4)^2 * (3/4)(2/4 :to ...
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1answer
22 views

How to find which treatment is most effective in gene data given one standard method and 3 variations

Sorry I am a biologist and it appears am not quite confident enough for statistical analysis. I have datasets that represent different treatments on a biological system. It records how many genes have ...
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1answer
22 views

Confidence interval of a uniform distribution

I need some help with the following problem: I want to estimate $n$ of $X_i \sim U(1, n)$ with a $90\%$ confidence level. What is given is the sample size with $10$ and the maximum of the sample with ...
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2answers
41 views

12 six-sided dice are thrown. What is the probability of getting each number twice?

I got this: $\frac{6!12!}{6^{12}2!^6}$ but the answer is this: $\frac{{12!}}{6^{12}2!^6}$ Im not sure I understand why you wouldn't write the $6!$ because if the first die's value is #3 then you have ...
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1answer
18 views

probability of a proportion point estimate

I've got a problem where I'm supposed to find the probability of a point estimate but cannot see how my answer is differing from the given one. The problem is: Unknown to an experimenter, the ...
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1answer
31 views

On a 50 question multiple choice exam with 5 choices per questions, What are the odds that I get 100% if I were to Guess every answer? [on hold]

What would the odds be to get 100% on a multiple choice exam where I guessed the answer to all 50 of the multiple choice questions (5 choices per questions)? A 1 in how many chance?
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0answers
14 views

LRT and Wald Test in Multivariate Linear Regression significance

I've been researching all afternoon trying to get a better idea of what the Likelihood ratio test and the Wald test are actually doing. I have a bunch of covariates and I'm testing out like 30 ...
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0answers
20 views

A Question about the Kurtosis

Problem: Show that if a binomial distribution with $n = 100$ is symmetric, its coefficient of kurtosis is 2.9. Answer: First, I am interpreting the term symmetric to mean that $p = q = \frac{1}{2}$. ...
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1answer
44 views

Question with excel [on hold]

Suppose I have a set of number like: 1,2,4,3,4,2,5,3,7,1,2,2 1) How can I make an histogramme with proportion on excel ? i.e. there is 4 number 2, 2 number 1... 2) add over the curve of the normal ...
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1answer
29 views

Geometric sum of geometric random variables

I am looking to find the probability mass function of $Y=\sum_{i=1}^NX_i$ where $X_i\sim\textrm{Geometric}(a)$ and $N\sim\textrm{Geometric}(b)$. I attempted to do this by finding the probability ...
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1answer
23 views

Hypothesis Testing? Probability

I'd be really grateful if someone can help me. I found this problem in the textbook Probability and Statistics by Wapole. This question look something similar to a Hypothesis test, but I have no ...
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0answers
22 views

Closeness in distribution implies closeness in statistics?

I am aware that convergence in distribution does not necessarily imply convergence in the mean. I browsed through some examples of statistical distances here ...
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1answer
24 views

estimate population size from samples

I don't think there is enough data to solve for this but wanted to run it by some folks smarter than me... So given the data below where classes are a sample of a professor's entire career, can you ...
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0answers
18 views

find the the deviation score of unknown score

I'm being asked to find a deviation score for the fifteenth score when only $14$ scores are given (given are deviations from the mean which are $+16, 0, -16, +1, +2, +3, +4, +5, +6, +7, +8, +9, +9$, ...
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61 views

Hottest Days of The Year

Recently, there has been much talk in the media of it being the hottest day of the year so far. It has always seemed to me that there are likely many more of these in the northern hemisphere than the ...
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1answer
26 views

Expected value of a sample

I am unsure of how to solve this question. I know from examples questions that expected value of a sample is usually very close to the population mean. However, it says to compute the expected value ...
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1answer
22 views

Variance of subset vs total variance

Is it true that the variance of subset is smaller than variance of the total set? Given each element in the set is a N-dimensional vector, and the distance is defined as Euclidean distance. Variance ...
3
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1answer
66 views

German Tank Problem, Confidence Level

Suppose you're in a city with n cabs. Each cab has a distinctive number from 0 to n. You take a cab 10 times, the choice of the cabs is independent and equiprobable. The cab with the biggest number ...
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0answers
18 views

counting , please help very urgent [on hold]

There are 7 teams (A, B, C, D, E, F, G) participating in a tournament. each team has 4 members. In how many ways can the 28 members be sitted in a row such that each of the members in team A are ...
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0answers
27 views

This random variable converges in distribution?

$\delta_x$ is a Borel probability that $\delta_x(x)=1$ and $\mu_n$ is a uniform distribution in this interval $(1, 1 + \frac{1}{n})$ The variable $X_n\sim \frac{1}{2}\delta_{\frac{1}{n}} + ...
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1answer
26 views

identifying sudden change in value given a list of values over time

I have a list of the average price of an item in a game over time. Things don't tend to move much. I am wondering how I can detect whether a new value inserted is a surprising movement in price. I ...
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0answers
10 views

Check trend for non-normal data?

I have data which is non-normally distributed time series. I want to find whether with time its increasing or decreasing. How will I check it. Earlier I thought of using t-test and linear fit. But I ...
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1answer
19 views

Significance of dummy variables in probit regression

I am an undergraduate student working on some projects using probit regression. I have a question on dummy variables that I was hoping someone could help me with (which I think stems from an ...
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0answers
15 views

Comparing Two Ways of Scoring Data [on hold]

I have used two different methods to give a score to the same data set. One is a discrete method and the other continuous. How do I show that the continuous method is more sensitive to changes in ...
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0answers
17 views

Establishing consistency

I need to establish the (weak) consistency of an estimator of the mean, $T=a+b\bar{X}$. I tried to apply Chebyshev's inequality, but I couldn't do much because the parameter that subtract in the ...
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1answer
16 views

Statistics probability [on hold]

A coffee shop sells 4 sizes with 4 different varieties. Customers can choose to add one or more syrups that come in 4 flavors. How many different coffees drinks can be made?
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0answers
15 views

Statistics question help! [on hold]

An insurance company classifies people to 3 groups: A, B, C. Also, according to company, the probability each group will be in an accident within a year of issuance is 0.05, 0.15, 0.3. If one person ...
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1answer
18 views

how to find the cumulative density function

Consider $$f(x)=3x^{-4} \qquad \mbox{on} \qquad x\geq 1.$$ Let $X$ be a continuous random variable on $x\geq 1$. Find the cumulative distribution $F(x)$ for $X$. I know that CDF for a continuous ...
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9answers
11k views

If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that it's an unfair coin?

Consider a two-sided coin. If I flip it $1000$ times and it lands heads up for each flip, what is the probability that the coin is unfair, and how do we quantify that if it is unfair? Furthermore, ...
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1answer
31 views

Statistics Probability [on hold]

Study shows 10% of household appliances fail during any given year. If a person has 4 household appliances what is the probability that exactly 2 of them will fail next year?
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0answers
22 views

Recursive Variance

What will be the distribution or features about the following $x$? $x=\mu+\epsilon$ where $\epsilon\sim N(0,x^{-1})$. It seems interesting in econometrics if we allow $x$ being a time series and ...
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0answers
17 views

Averaging averages and standard deviations

I am comparing exam scores for different subjects: physics, biology, english. I am looking at what proportion of the curriculum is spent on each subject. The number of students is fixed: the same for ...
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0answers
40 views

Proving linear algebra equation [on hold]

I am having trouble proving that two multivariate formulas are equivalent. I implemented them in MATLAB and numerically they appear to be equivalent. (This problem comes from Bayesian estimation, ...
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3answers
39 views

You roll 3 six-sided dice. What is the probability that the third is at least as high as the highest of the previous two?

I know that the probability of the first two dice being different is $\frac56$, and the first/second being greater is $\frac56$, but am not sure how to calculate the prob of the 3rd being greatest. ...
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0answers
20 views

business math question

Diane Van Os decided to buy a new car since her credit union was offering such low interest rates. She borrowed $33,600 at 4.25% on December 16 2012, and paid it off March 17 2014. How much did she ...
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20 views

Likelihood of large difference in averages

Note that I updated question because initial example grades did not satisfy the overall average that followed from the numbers given in the article. A newspaper artticle in Norway made me curious ...
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0answers
29 views

Interpolation at “extreme values.”

I am working with a meteorologist on a project. We are pulling data from METAR Observation stations on several variables (such as temperature, dew point, wind speed, etc.) throughout time. ...
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0answers
18 views

How to measure the stability of datas

The background: I have a server handling $n$ kinds of requests, denoted by $k_1, ..., k_n$, at a certain time, many requests has been processed, the average time it takes to process $k_i$ is $t_i$, ...
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2answers
34 views

Tabulate the probability distribution of $x$.

If a red dice and a green dice are rolled together and $X$ is the highest score minus the lowest score of the dice, what are the possible values of $X$? Tabulate the probability distribution ...
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3answers
62 views

Sample space: What's the possibility that a family has n boys?

What's the sample space in these two cases? Case1: Of all families with two children you ask the parents, if they have a boy born on a Thursday. They say yes. What's the possibility that the family ...