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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Poisson(Exponential) Distribution question

I am trying to solve the following question: If the number of calls received per hour by an answering service is a Poisson random variable with rate of 6 calls per hour, what is the probability of ...
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10 views

Extreme value distributions of unaccountably infinite set of random variables

Let us suppose that we have an uncountably infinite set $A=\{x_1,x_2, \cdots\}$ of i.i.d. random variables $x_i$, say with gamma distribution. Are minimum and maximum extreme value distributions ...
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20 views

Statistical significance of difference between samples given total success rate when test was applied by group

I am comparing treatments that select members to receive some email, and we are measuring the response to that email. The emails are similar, but are sent to a different group of members and a ...
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0answers
12 views

how to find the corelation or regression between two tables [closed]

I have two tables , I need to find the dependence or relation between these two tables table one ... $3$ sport v/s four regions with value as sales table two .. same $3$ sport v/s same four regions ...
0
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1answer
27 views

Partition-based entropy of a sequence

The entropy $H$ of a discrete random variable $X$ is defined by $$H(X)=E[I(X)]=\sum_xP(x)I(x)=\sum_xP(x)\log P(x)^{-1}$$ where $x$ are the possible values of $X$, $P(x)$ is the probability of $x$, ...
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0answers
13 views

Most appropriate ranking system

Imagine a system has N set of attributes, all with values of 1-20 (20 being desirable). There are a set of tests which can be performed on the system, each assessing a unique subset of the attributes. ...
0
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1answer
19 views

Confidence Interval w/ true standard deviation?

I'm very scared that my calculations I did were wrong. Here is why: I assumed true standard deviation meant population S.D. However the question says the standard deviation is from a sample. So what ...
-3
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1answer
43 views

Statistics(central tendency) [closed]

The scores of students in a Mathematics examination is normally distributed with a mean of 60 and a standard deviation of 8. a. How many percent of the examinees got ...
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16 views

What's the difference between Error Analysis, Statistics, and Probability?

I am interested in what people think about this question. What is the difference between error analysis, statistics, and probability? Error analysis is not a discipline that you can find in a ...
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2answers
16 views

statistics question about two random variables

Two random variables $X$ and $Y$ have the following joint pdf: $$f(x, y) = \begin{cases} \frac35x(y + y^2) & \text{if }0<x<2\text{ and } 0 < y < 1\\ 0 & \text{otherwise} ...
2
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1answer
14 views

The distributions of incomes in two cities follow the two Pareto type pdfs. Find P(X<Y)

The distributions of incomes in two cities follow the two Pareto type pdfs $$f(x)= \frac{2}{x^3}, 1 < x < \infty.$$ $$g(y) = \frac{3}{y^4}, 1<y<\infty.$$ Here one unit represents ...
0
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1answer
11 views

Normal Distribution $r-1$ th moment with absolute value

I was stuck for this problem whole night and I tried numerical solution using MATLAB and the following result seems hold for x follow normal N(0,1) and for any positive number (not integer only) ...
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2answers
24 views

How to I use the standard normal table to get the following Z value?

So I am given that $P(X \le 31.5) = 0.05$ and according to the textbook, after standardizing and using the standard normal table we get $$(31.5 - \text{mean})/(\text{standard deviation}) = ...
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0answers
57 views

Benchmarking runner speeds [closed]

I have collated the times my 400 mtr runners have run over a period of time. Logically some are faster than others and some races are run differently (less speed first 200 ) Is there a mathematical ...
2
votes
1answer
59 views

sample variance of regular polygon upon superimposition of vertices

Given, the vertices of a regular polygon, the centroid here would be the sample mean of the vertices and we assume it to be at the origin. The distance from each vertex to centroid is ...
-1
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0answers
23 views

Sampling distribution for sample mean and sample variance in case of Normal population [closed]

Let $X_1,X_2...,X_n$ be a random sample drawn from $N(\mu,\sigma^2)$ popultion. Further let $\bar{X}$ and $S^2$ be sample mean and sample variance respectively. Then Find the joint PDF of ...
1
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1answer
50 views

Probability of being the millionth customer (What Would You Do?)

I saw this episode of "What Would You Do?" a few months ago, and I keep wondering what would statistically be the best thing to do in this situation. Here is the problem formulation: You are waiting ...
2
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2answers
38 views

How do I rate smoothness of discretely sampled data? (Picture!!!)

In the sense that the following curves pictured in order will be rated 98%, 80%, 40%, 5% smooth approximating by eye. My ideas: (1) If the curves all follow some general shape like a polynomial ...
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0answers
10 views

How close is $\operatorname{argmax}_p E[\log(f(p,\alpha)]$ to $\operatorname{argmax}_p \log(E[f(p,\alpha)])$?

Here $\alpha$ is a random variable and the expectation is taken with respect to that variable. I am wondering if it's the same in any case or there's a theorem quantifying how close both things are. ...
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1answer
18 views

Isolate Sigma and FWHM from gaussian

I have the Gaussian: $a e^{-b^2 (x-c)^2}$ And need to isolate the Sigma and FWHM from it. I believe that $b = \frac{1}{\sigma^2}$ and $FWHM = 2.354(\sigma/2)$ However, I need to program this ...
0
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1answer
42 views

Current applications of the central limit theorem for binomial distributions

The central limit theorem in the binomal distribution case, also known as the De Moivre–Laplace theorem was historically used to approximate the binomal distribution with the normal distribution. I ...
0
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1answer
23 views

find the probability that the amount of milk produced is between 45.9 gallons and 50.3 gallons. [closed]

the amount of milk produced each day by a herd of cows is uniformly distributed between 44.6 gallons and 58.8 gallons. find the probability that the amount of milk produced is between 45.9 gallons ...
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0answers
26 views

How is the Variance of this estimator equal to $\theta$?

Currently going through solutions of a worksheet and I don't understand the jump between two lines of working. "$\hat{\theta}_1$ and $\hat{\theta}_2$ are independent unbiased estimators for an ...
0
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1answer
20 views

proportion confidence intervals

Here is a question from my introductory statistics course. What is the sample size necessary for a two-sided $90\%$ CI for the population proportion $p$ to have a width of $0.2$ when no prior ...
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0answers
39 views

% Relation of the Total

I have two factories Production Target Factory A 121.58 126.41 Factory B 110.62 106.45 If ...
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0answers
31 views

Expected value of discrete uniform variable

I have a question regarding linear combinations/transformations in statistics. I'm quite sure the answer is relatively easy, but I can't seem to find a solution that corresponds to my solution manual. ...
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0answers
20 views

Derivative of a correlation function

From a big set of data I create a correlation function between a response parameter and three input parameters $(P_1, P_2, P_3)$. $Response = K_1 + K_2 \cdot P_1 + K_3 \cdot P_2 + K_4 \cdot P_3 + ...
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2answers
49 views

If we know X is a Poisson binomial random variable what can we say about mX?

Suppose that X is sum of m independent Bernoulli random variables that are not necessarily identically distributed, and thus it has Poisson binomial distribution. Is mX also a Poisson binomial random ...
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0answers
40 views

PCA “Compact Trick”

This is my first time asking a question on here, so forgive me if I broke any etiquette! My question is related to a question asked here. To paraphrase what is mentioned in the link, consider a ...
1
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1answer
40 views

Computing $E[ {\rm Tr}\{(ZZ^T)^2 \}]$ for $Z$ Gaussian.

Let $Z \in \mathbb{R}^n$ be a Gaussian random vector with zero mean and $Cov(Z)=I$ where $I$ is identity matrix. How to compute \begin{align*} E[ {\rm Tr}\{(ZZ^T)^2 \}] \end{align*} I know that ...
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0answers
22 views

How do I find middle range with normal distribution?

I am currentLy reading my textbook there is an example that I cant understand. Can someone explain to me the hint given to solve it? Q. Verbal SAT scores follow normal(430,100) distribution. What is ...
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1answer
17 views

Statistics and data analysis

What is meant by confidence interval in data analysis e.g. 95% confidence interval? How does p<0.05 estimate significant difference?
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1answer
48 views

1 scratch off, 1 ticket or both? [closed]

I have a problem that I would like some input on. Free beer(or soda) for best answer. I have several scratch offs and several tickets options. I have the maximum loss(item price) and I have the ...
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1answer
28 views

Proportion with standard deviation and mean [closed]

Suppose a tire manufacturer makes a tire with a lifetime that is approximately normal with a mean of 70,000 miles and a standard deviation of 4,400 miles. What proportion of the tires will last at ...
0
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1answer
21 views

Check if the weak law of large numbers holds true for the following sequence of random variables

Suppose we have $n$ independent discrete random variables, whose distribution is as follows: $X(k)$, where $k$ is any integer from $1$ to $n$, can take any of three values: $-\sqrt{k}$ with a ...
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17 views

distribution function from a sample

I have a sample about relative error of a measuring device and I wanna know the error probability of that device. What non parametric test must I use to know its error probability distribution of the ...
1
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1answer
32 views

What is the probability density function of **the multiplication of Gaussian variables**?

Assuming $x_1,x_2,\ldots, x_n$ are $n$ independent variables from standard Gaussian distribution $N(0,1)$. Then we construct a new variable by $y=\Pi_{i=1}^n x_i$. Can anyone show the probability ...
0
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1answer
40 views

Combining normal distrubutions

I am not sure of the terminology here, if this is a product, summation, or average. How can you take a two unimodal normal distributions and combine them into a bimodal distribution? And then combine ...
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55 views

5 girls and 3 boys are arranged randomly in a row. Find the probability that…

5 girls and 3 boys are arranged randomly in a row. Find the probability that: a) the 5 girls are next to each other,= 2/28 b) the 3 boys are next to each other,=3/28 c) there is one boy on each end, = ...
4
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1answer
47 views

Which math class can I take to learn how to derive statistical models

I have taken several stats classes and. Have seen many models in action like the normal, poisson, dirchet, etc. and seen several inference tests in action like chisq, ttest and anova. However I'm ...
0
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2answers
34 views

Difference between two proportions in a Confidence Interval

Ten engineering schools in the United States were surveyed. The sample contained $250$ electrical engineers, $80$ being women; $175$ chemical engineers, $40$ being women. Compute a $90\%$ confidence ...
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1answer
38 views

Proportion confidence interval [closed]

everyone. here is a question from my introductory statistics course in university about proportion confidence interval. Two hundred students are each asked to compute 95% CIs for a population mean ...
4
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1answer
39 views

Monopoly Game Statistics

I was playing a game of monopoly the other day, and in the course of strategizing I came up with the idea that how 'safe' you were in the game was a matter of what your expected income/outcome was as ...
0
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1answer
17 views

A sample of 50 fluorescent light tubes from the SLT Company has a mean life of 20.5 hours and a standard deviation of 1.6 hours. Test: [closed]

A sample of 50 fluorescent light tubes from the SLT Company has a mean life of 20.5 hours and a standard deviation of 1.6 hours. Test: i. At the 1% level whether the sample comes from a population ...
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0answers
31 views

How to prove: $E(|tr(x^Tww^Ty)|^k)\leq \|yx^T\|_2^k E(tr(x^Tww^Tx)^k)$?

How to prove: $$E(|tr(x^Tww^Ty)|^k)\leq \|yx^T\|_2^k E(tr(x^Tww^Tx)^k)$$, where $k$ is a positive integer, $x,y$ are fixed vectors, each entry in $w$ i.i.d. follows from an standard norm ...
0
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1answer
23 views

Generalization of method of least squares to matrix system (Pseudo inverse?)

A and B are two m$\times$n real matrices with m > n. I need to find X: a real m$\times$ m matrix such that $\| A - X B\|$ is minimized. On thing I'm thinking about is using the singular value ...
0
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1answer
15 views

The sample distribution (pdf) of the sample mean retrieved from gamma distribution

Is it true that the sample distribution (pdf) of the mean where sample is of size n retrieved from a gamma distribution with shape a and scale b is given by ...
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0answers
11 views

DRIFT MATRIX in Ornstein Uhlenbeck Process

The Weiner Process was unable to explain Brownian Motion and then there was the need of Ornstein-Uhlenbeck Process. The Ornstein-Uhlenbeck Process describes the Brownian Motion in the presence of ...
3
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2answers
139 views

Why are these following variance and expected value computations legitimate?

I spent over an hour of my exam's given time to calculate the variances and expected values as given here: Let $p,q\in (0,1)$. The number of costumers entering a supermarket is a r.v. $X$ with ...
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1answer
34 views

About 'Marcinkiewicz–Zygmund inequality'

Marcinkiewicz–Zygmund inequality gives gives relations between moments of a collection of independent random variables. The statement of this inequality can be seen in Wiki ...