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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77 views

To sample or not to sample?

I have the following issue (I want to predict sports results). Let $X$ be a discrete RV with $m$ possible outcomes, each having probability $p_i$, for $i=1,\ldots,m$. Assume that I have a large iid ...
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1answer
16 views

Maximum likelihood estimator transformed parameter

I don't get the gist of b). What is it that we are in fact calculating here? I don't get why we can just plug in the rearranged formula.
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3answers
37 views

In how many ways can 4 girls and 3 boys sit in a row such that just the girls are to sit next to each other? Answer: 288

In how many ways can 4 girls and 3 boys sit in a row such that just the girls are to sit next to each other? Answer: 288 Please explain how to get this. I understand that we have GGGG => 4 ...
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1answer
31 views

Sum of independent random variables (conditional prob.)

When $X_1,...,X_{k+l}$ are independent random variables with $P(X_n=1)=p$ and $P(X_n=0)=1-p$, ($n=1,..,k+l$), and $B=X_1+...+X_k$ and $C=X_1+...+X_{k+l}$, what is $P(C=n|B=m)$ for $n=0,...,k+l$ and ...
2
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0answers
24 views

Probabilities of this blackjack hybrid

I am currently trying to study a hybrid / simplified version of Black Jack but as i am not as good with probabilities i am hoping that i could receive some advice about the probabilities behind the ...
0
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1answer
18 views

When residual standard error is equal to standard deviation of dependent variable in linear regression?

I wonder when residual standard error is equal to standard deviation of dependent variable in linear regression? Could someone provide some information on this topic and explanation?
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1answer
26 views

x in the range of a random variable $X$ implies the pdf $f_X(x)>0$

Let $\mathcal X$ be the range of a continuous random variable $X$. Next, let $x\in\mathcal X$. If $f_X$ is the pdf of the random variable $X$, how can I prove that $f_X(x)>0$?
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1answer
32 views

Sampling distribution of a Random Variable [closed]

Let the population X, defined by X~Ber(p); Find The sampling distribution of an RV. $\bar{X} = \frac{1}{n}\sum_{i=1}^{n} Xi$ where Xi is the obtained value from an extraction with reposition of this ...
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1answer
43 views

Independent Events or Random Variables

First recall the following definition of independent random variables. Let $(X_t)_{t \in \mathcal T}$ be a set of random variables, where $\mathcal T$ is an arbitrary index set. Then $(X_t)$ is ...
0
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0answers
17 views

What is The Basis for The Similarity Of Distance And Standard Deviation?

The common way to think about distance is Minkowski difference with the special case $r=2$. The definition for standard deviation is $ \sqrt{\frac{1}{n-1} \sum (x_i - x)^2}$. Both of these definitions ...
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1answer
10 views

Using sampling for p-value computations

I have a search algorithm against a genomic sequence that attach a score $s$ for each search result. I want to provide a p-value score for each result: the procedure I currently use is to search the ...
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2answers
39 views

“Show experimentally” that for large $N$, $X$ appears to be normally distributed.

I'm a bit confused about the following problem: Let $X$ be the random variable $$X = \frac{X_1+X_2+...+X_N}{\sqrt{N}}$$ where $X_k$ is the outcome from the $kth$ flip of a fair coin where heads ...
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1answer
17 views

Understand the English paragraph on association rule.

I am currently studying Association Rule Pattern Mining. I am reading the explanation on wikipedia about it. Somehow, I feel like I have a problem in understanding the paragraph below. Can somebody ...
0
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0answers
13 views

Question about the poly-Euler preprint

I'm looking over the preprint on poly-Euler numbers, and I think there might be a typographical error on the third line because $j=0$ leads to a discontinuity. Could somebody explain the substation ...
0
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0answers
18 views

Statistical Test for seeing differences in a single sample [migrated]

So I've been trying to analyze 3 repeats for some data (essentially, a single independent variable measured at three different times), which would look like something like this: Test 1 [Value] Test ...
0
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1answer
13 views

When using the geometric mean to compare data with different ranges, how do you include a binary piece of data?

For instance, if you were comparing 10 companies on 3 categories, with the first category having a range of 1-5, the second having a range of 1-100, and the third being either 0 or 1. All three ...
2
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1answer
16 views

Looking to assign percentage contribution among 4 variables in a simple equation

I have a seemingly simple problem, that is giving me some trouble in solving. I have a 4 variable equation and want to determine the contribution of each variable in moving the dependent variable from ...
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1answer
15 views

How do I compare how much variation there is between data sets?

I have a large number (~1000) of number sets containing 8 numerical elements. Here's an example: ...
0
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1answer
29 views

Is the sum of predicted y values equal to the sum of actual y values?

Say I have a set of points Y and I want to accuratly predict the values of Y by using three variables X1,X2,X3. Hence my equation is Y=intercept + C1*X1 + C2*X2 + C3*X3 After performing linear ...
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1answer
11 views

Working out a parent percentage from child percentage

I am currently working on a performance indicator system for the number of reviews due on a bunch of document against the number that were due in that month as a percentage. There are several areas ...
0
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0answers
33 views

interpretation of ANOVA using RStudio

This is my first post so go easy on me... So I have this table as 'tomato' and I have come up with some linear models to try out which are given below... however I don't know how to interpret the ...
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0answers
18 views

What is the log of slop says [duplicate]

What's the meaning of the following?? "$F(x)=\frac{\log(p)}{\log(q)}$ Where $p$ and $q$ are the slope of the point in the non linear graph $(x_1,y_1)$ and $(x_2,y_2)$ and $q$ is the slope of ...
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0answers
12 views

Mean and SD of an approximate distribution?

Define the rv X to have a discrete uniform distribution. If a normal six-sided die is rolled and we are interested in the probability that the third face 4 appears on the K-th roll. Determine the ...
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0answers
27 views

whats the meaning of log of the slope says

whats the mean of the following $F (x) = \log(p)/\log(q)$ Where $p$ and $q$ are the slope of the point in the non linear graph $(x_1, y_1)$ and $(x_2, y_2)$ and $q$ is the slope of $(x_2, y_2)$ and ...
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0answers
26 views

Multiple correlation

My question is very elementary. I need to implement a software that computes the multiple correlation of a set of datas that I have. In order to do that, I need would like to find the generic formula ...
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1answer
35 views

Markov/Chebyshev's inequality Problems

Let $X$ and $Y$ be two random variables for which $ E(X)=75 $, $ E(Y)=75 $, $\mathrm{var}(X)=10$, $\mathrm{var}(Y)=12$, $\mathrm{cov}(X,Y)=-3$ (i) Find and upper bound to $P(|X-Y| \ge ...
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0answers
13 views

Statistical study of the effectiveness of this site [migrated]

Is there a statistical study of how many questions on this site get answered immediately or fairly quickly and correlated with the difficulty of the question or where it occurs in the academic study ...
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0answers
31 views

what the given equation want to say

Sir read one research paper in which they are calculating threshold in host by the following equation. I would like to know is this equation is working and how. In the virtual environment each host ...
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2answers
46 views

Approximate distribution for the sample mean?

A random variable $X$ is said to follow a discrete uniform distribution if its probability function is given by $$p_X(x) = \left\{ \begin{array}{ll}\frac{1}{\theta}, & x = 1, 2, \ldots, ...
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1answer
28 views

Limiting distribution.

Let $Y_n \sim \chi^2(n) $. Find the limiting distribution, $(Y_n-n)/ \sqrt{2n}$ as $n\rightarrow \infty $, using moment generating functions. I don't know how to properly calculate the moment ...
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26 views

Asymptotic Bounds for the distribution of $f_n(X_n)$.

Let $\{X_n\}_{n \in \mathbb{N}}$ be a sequence of $\mathbb{R}^{k}$-valued random variables defined on some probability space $(\Omega, \mathcal{F}, \mathbb{P})$ converging almost surely to $X$. ...
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1answer
25 views

Proving conditional independence

I have the following problem: Three random variables have the following joint distribution: $$ P(X,Y,Z) = P(X)P(Y|X)P(Z|Y) $$ Show that $X$ and $Z$ are conditionally independent given $Y$. The ...
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0answers
16 views

Appropriate statistic and application of results?

I have historical data (by month) for several years. Each month includes DV data for total dollars of margin. IVs include sales price per unit, number of units per invoice, total number of invoices, ...
0
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1answer
46 views

The Weibull as the limiting distribution of the Burr distribution

I often deal with "payout patterns" which are vectors of the cumulative percentage of a loss that has been paid over time. For example, for $t \in [0, 1, 2, 3, 4, 5]$ I may have $p_t = (5\%, 15\%, ...
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1answer
47 views

MGF Of a Normal-Gamma Distribution

According to wikipedia, the normal-gamma distribution is actually, unconditionally, a nonstandardized t-distribution. The MGF of t-distributions do not exist. However, I can make the following ...
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0answers
15 views

Population confidence interval from sample SD and sample mean?

A sample has: $$\text{a sample size } n = 70,$$ $$\text{sample standard deviation } s = 184.43,$$ $$\text{and a sample mean } \bar{x} = 564.15.$$ Compute a 95% confidence interval for the population ...
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1answer
24 views

Marginal pdf $f_2(y)$ is proportional to $g_2(y)$.

The question in DeGroot's Probability and Statistics is: Given the joint pdf of X and Y, $$f(x,y)=\begin{cases} c\sin x, & 0\le x\le \pi/2, 0\le y\le 3\\ 0, & \text{otherwise} \end{cases}$$ ...
0
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1answer
17 views

Getting the pmf from probability generating function?

I uploaded a picture so that my question may be accurate. It is question 3a that I am struggling with. I've learnt that the P(X=r)is the rth derivative(w.r.t. t) of the pgf at t=0 . Divided by r ...
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0answers
14 views

Searching for some kind of question in statistics

I'm now preparing exams for mathematical statistics. Our teacher told us that there will be problems concerning the estimator for vectors(or matrices) that increases length when the number of samples ...
0
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1answer
48 views

How to bell curve

My mom is a teacher, and her kids failed a test. Suppose that her class had a mean of $x$. How would she be able to curve a the marks such that: 1) The mean is 60 2) No mark exceeds 100% Thanks
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1answer
29 views

Best way to handle the ratio which cannot be represented as floating point numbers.

I need to calculate the ratio of the form: $s=\sum_1^3q_i$,$\quad$ $p_i=\frac{q_i}{\sum_1^3q_i}$, where $q_i >0$. One problem is that $q_i$ are too small that they can not represented as ...
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0answers
10 views

Expressing the F-statistic by t-statistics

Consider the regression model $Y=X\theta+U$, whereat $X$ is a $n\times k$ - matrix with $\text{Rank}(X)=k$. Furthermore $U\sim N(0,\sigma^2 I_n)$ with $\sigma^2>0$. We consider the case of ...
0
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0answers
27 views

independence at equal and different times

this is a question about stochastic processes. Let's call $A(t)$ and $B(t)$ two stationary processes and denote by $E[*]$ the expectation value. Suppose we know that $E[A(t)B(t)]=0$ for every $t$. The ...
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0answers
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Injective uniform distribution on an n-sphere

I just asked this question on the stats stackexchange, but I thought that maybe someone on math knew the answer. So: For an application I'm working on, I need to go from some uniformly distributed ...
2
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1answer
40 views

probability in roulette!

So I have read how to play roulette...still a little confused, and now I'm faced with a probability question about it which makes the problem a little harder. Please help me reason this where ...
2
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2answers
52 views

Expectations and variance with rolling a dice 10 times

Let's say you roll a fair dice 10 times and X is the number of sides that never show up. (i.e. Roll 1 - 10 = 1424145221, X = 2 because 3 and 6 never show up) Values of $N=0,1,2,3,4,5.\\ P(N=6) = 0$ ...
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2answers
24 views

A joint PDF question: $\displaystyle f(x,y)=1-\frac x3-\frac y3$

Really stuck on this problem: If $\displaystyle f(x,y)=1-\frac x3-\frac y3$ for $0 \le x \le 2$ and $0 \le y \le h,$ the find $h$. I know I need to integrate but confused how to set it up. ...
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0answers
12 views

Conditional Expectation, Orthogonality, and Correlation

I know that if $\epsilon$ and $x$ are independent, then $E[\epsilon|x]=E[\epsilon]$ and Cov$(\epsilon,x)=0$. However, $E[\epsilon|x]=E[\epsilon]=0$ implies Cov$(\epsilon,x)=0$ iff $\epsilon$ and $x$ ...
2
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2answers
36 views

probability, expectation, variance

A 10-digit long number is picked randomly and each digit's pick is independent and has an equal probability of being picked (1/9 because there's digits 1 to 9). Let $X = \#\{\text{missing digits}\}$ ...
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1answer
26 views

Expectation: E(X-Y) and Variance: Var(X-Y) in statistics

There are $n$ students and you pick a student replacement so each pick is independent . $p$ is the portion of the student body that will vote for A instead of B for student council president. Let $X ...