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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Statistical Problem (part 2)

Following my question I found another problem. Having the same data from the other question: There are 2 melon stores. The melon weights follow a normal distribution. Store A -> μ = ...
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127 views

Normal distribution, statistical problem

Before proceeding to the question, bear in english is not my native language and therefore technical terms may be wrong. So, I'm trying to solve the old exam question, and I have different results ...
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1answer
235 views

Relationship between two random variables?

What is the relationship between a random variable obeying the subexponential distribution defined here and a random variable $X$ satisfying $P\left(\left|X\right|>t\right)\le\alpha e^{-\beta t}$ ...
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1answer
61 views

How to find optimal border that defines, who is “friend”

I have the data about usage of several services in the population and the data about interactions among users. The idea is to determine, who is user's friend and who has interacted just ...
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1answer
249 views

Well known probability distributions defined on a $n$-dimensional simplex besides the Dirichlet distribution?

Are there well known probability distributions defined on a n-dimensional simplex besides the Dirichlet distribution where the variation of of each component doesn't vary as much when the mean of the ...
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1answer
47 views

arctic sea ice data by year

I want to demonstrate the usefulness of regression lines to my class, and I was hoping to do so with some data about the Arctic sea ice. What I'd like is the maximal area covered by the ice per year, ...
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0answers
47 views

Cauchy Random Variable Question [duplicate]

Possible Duplicate: How calculate the probability density function of $Z = X_1/X_2$ Need help with the following problem: Suppose that X and Y are independent normal random variables with ...
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1answer
163 views

Maximize expected heads with biased coins.

Say I have n biased coins. Coin $i$ lands on heads with probability $p_i$ which comes from a uniform prior probability distribution over $[0, 1]$. At times $t = 1, 2, ..., k$ I must select one of the ...
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1answer
362 views

How do I calculate the aposteriori probability distribution for someone's answer to a poll being an approval?

Imagine I'm polling a random sample from the population and it asks them if they approve of the President or not. I also ask them some categorical demographic questions (age-bracket, race, gender, ...
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1answer
212 views

cumulative probabilities for standard normal density vs confidence interval

Lets say I have a 90% confidence interval. It's Z score is 1.645 (so 90% of values are between -1.645 and 1.645 standard deviations from the mean) and and it's got error margin of 5% in each tail of ...
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2answers
172 views

Determine the MLE of parameter $\theta$ [closed]

Suppose $X_1,\ldots,X_n$ are a random sample of distribution with probability density function $$ f(x) = \begin {cases} \frac{\theta}{2} & \text{}\ x=-1,1 \\ 1-\theta & \text{} \ x=0 \end ...
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2answers
119 views

How does one find $E\Bigl(\frac{(\sum_{i=1}^nX_i)^2}{\sum_{i=1}^n X_i^2}\Bigr)$

Suppose $X_1,\ldots,X_n$ are a random sample of $N(0,\sigma^2)$. How can find $$ E\left(\frac{\bigl(\sum_{i=1}^nX_i\bigr)^2}{\sum_{i=1}^n X_i^2}\right) $$
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0answers
46 views

Symmetrizing a sequence of vectors

Given a finite set of real numbers $X_1, \ldots, X_n$, we can compute the first $n$ power sums of these numbers. From the power sums, the set $\{X_1, \ldots, X_n\}$ can be recovered. Essentially we ...
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1answer
81 views

Hmm. help with a tiny statistics question please

This isn't homework, I am boggling my head over it though. I got all sorts of answers, just not the answer my book demands. For what value of $x$ the mean of the given observations $2x - 5, x + 3, 7 ...
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4answers
235 views

Rounding non-integer values to integer values without causing an 'overflow'

The following problem comes from a piece of software I am currently working on, but since it's partially a mathematical problem, I'll ask the question here. In my application I have a fixed value ...
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1answer
988 views

Calculating percentage

I'm wondering if my answer for C would be correct and if I was understanding A correctly? I heard drawing venn diagram could help but I'm not sure how to convert the numbers to a diagram. A ...
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1answer
234 views

Example of a joint density function $f(x,y)$ such that $E(Y|x)=\ln(x)$:

Let $X$ and $Y$ be jointly continuous random variables with $X$ taking values in some $D$. Give an example of a joint density function $f(x,y)$ such that $E(Y|x)=\ln(x)$: I have tried so many ...
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1answer
475 views

Whats the probability that a certain amount of batteries life longer than 3.25 hours?

The mean and standard deviation of the lifetime of a battery in a portable computer are 3.5 and 1.0 hours respectively. So, what is the probability that the mean lifetime of 25 batteries exceeds 3.25 ...
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1answer
340 views

Given a set of data (distance vs time) obtain a closer approximate for velocity

This is actually a physics experiment. I've collected a set of data Distance and time it takes for a cart to move down an incline plane. From here, I've calculated the average time (...
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1answer
81 views

N-P Lemma Test in Hypothesis testing and significance of inequality sign.

For the hypothesis test: H_0 : mu= mu_0 (mu_1 > mu_0) H_1 : mu= mu_1 Applying N-P Lemma: {X: lambda(mu_0,mu_1;X)>= k} Where lambda(mu_0,mu_1;X) is the ratio of likelihood functions; with the ...
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1answer
50 views

Probability and statistical analysis

The probability of a missile hitting the target successfully in a trial is 0.2. Five successful hitting are needed to destroy a particular target. What is the probability that the target will be ...
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2answers
70 views

Statistical Analysis and Techniques

The lifetime in hours of a tubelight is a random variable $X$ having a probability density function $f(x) = 4xe^{-2x}$, where $x>0$. If $Y= -3X+10$, then find the Expected Value of $Y$, and ...
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269 views

What is a confidence interval?

What are the nature and purpose of confidence intervals?
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2answers
155 views

Why $\Delta(c^2)=2c(\Delta c) $?

I read a solution of find relative error for $c^2 = a^2 + b^2 -2ab\cdot\cos(\alpha) $ and it written there the equation $\Delta(c^2)=2c(\Delta c) $ .can someone explain how to developing this equation ...
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1answer
851 views

Finding the MLE for parameter $\theta$ from distribution of the form $e^{-|x-\theta|}$

this is my first post so I apologize if the formatting is a little rocky. I'm currently going through "Probability and Statistics" 4th ed by DeGroot/Schervish, and I was wondering if somebody could ...
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2answers
564 views

Trends in the distribution of reordered digits of Pi (OEIS A096566)

First let me try to describe in more details below the approach of "reordering" digits of Pi, which is used in OEIS A096566 https://oeis.org/A096566 and what I have done analyzing it so far. I am ...
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4answers
2k views

What does it mean when a statistician says I’m 90% confident that the mean of the population is between 1 and 9?

Does that mean if I draw samples from the population that 90% of the time I'll get a number between 1 and 9? Added: assume normal distribution for the population.
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1answer
115 views

Trying to understand LMS algorithm

This is what's written: So, $h(x)$ is basically a linear function to predict values of some training set. I understand everything that's happening up to the point where we take the partial ...
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1answer
119 views

Finding $E\Bigl(\overline{Y^2}\Bigm|\overline{Y\vphantom{Y^2}}\Bigr)$ by Basu's theorem?

Suppose $Y_1,\ldots,Y_n$ are a random sample of normal distribution $\mathcal{N}(\mu,1)$. If $\overline{Y^2}=\displaystyle\frac{1}{n}\sum_{i=1}^n Y_i^2$, how can I find ...
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1answer
153 views

I am trying to prove the identity $ \sum_{k=m}^{n} k^{\downarrow m }{n \choose k} = n^{\downarrow m } 2^{n-m}$

Prove algebraically $\sum_{k=m}^{n} k^{\downarrow m }{n \choose k} = n^{\downarrow m } 2^{n-m}$ I have an idea as to how to prove it when m = 1, but am having trouble otherwise. When m=1, we just ...
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4answers
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How many times to roll a die before getting two consecutive sixes?

Basically, on average, how many times do you have to roll a fair six-sided die before getting two consecutive sixes?
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1answer
111 views

Counting number of correlations between n variables in a set

Suppose I have a set of 40 variables {A, B, C...} I want to count the number of possible correlations for n variables. For example, if n=2 I have 40(40-1)/2=780 correlations How do I do it for n ...
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1answer
198 views

Stats brainteaser - How to find out how many marijuana smokers there are on campus with discreet survey

You want to find out how many students on campus smoke marijuana. However, you don't want to just go up and ask them if they smoke pot, as they might be embarrassed or lie for some other reason. ...
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57 views

Is there any significant Geometric/analytic property of the Pearson coefficent that could be applied to statistics?

Is there many significant Geometric/analytic property that the Pearson coefficent has which could be applied to statistics? It seems very interesting to me. Thanks in advance.
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1answer
58 views

How to derive the equations in 3:19-3:30 provide in a MIT opencourse ware lecture about the least square method?

How to derive the equations in 3:19-3:30 provide in a MIT opencourse ware lecture about the least square method? Link: http://www.youtube.com/watch?v=YwZYSTQs-Hk Thanks in advance!
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1answer
2k views

Understand simple problem on inflation

If the average food basket costs $100$ euros at 2nd quarter prices, how much will it cost for 3rd quarter prices? Below is the graph. I know that the answer is $97$ and can be achieved using follows: ...
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1answer
180 views

Continuously sampled event: Estimating the value of a future data point, based on past measurements and their tendency

Problem I'd appreciate some ideas on how to define a formula to estimate the value of a future data point for a continuously sampled event, based on past measurements and their tendency. At any ...
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2answers
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Probability HIV diagnostic test is right

Hi everyone I would I really appreciate if anyone could help me out with this problem. I was discussing it with a friend and we disagreed on whether we needed to treat this as a conditional ...
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1answer
72 views

Probability distribution for a function of a random variable

I have the distribution of X with respect to parameter t vaying between 0 and 1. However, in nature, parameter t is not uniformly distributed. It has a known probability distribution. What is ...
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5answers
3k views

What about without replacement

Cards are drawn at random and with replacement from an ordinary deck of 52 cards until a spade appears. what is the probability that at least 4 draws are necessary. Is this idea correct. The ...
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1answer
147 views

Probability / statistics calculation

Lets say I have a series of 100 digits forming a number. 15 of those digits are always the same at the same place, 85 of those digits are randomly 1 to 5. I generate 10000 numbers this way. What would ...
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3answers
1k views

conditional probability that both answers are correct given that at least one is correct

I came across this question whiles doing conditional probability and need a vivid explanation. A person answers each of two multiple choice questions at random. if there are four possible choices on ...
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1answer
913 views

Meaning of Empirical formula when applied to some cases

When applying the Empirical formula on a data set, for example calculating 1, 2 or 3 standard deviations below and above the mean of a data set, for some cases, this might not make sense. For example, ...
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1answer
199 views

Probability of at least 2 kings given 3 kings

Just need a help hand, I just want to know whether I'm doing the right thing for this question. A hand of 13 cards is to be dealt at random and without replacement from 52 cards. find the conditional ...
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2answers
143 views

Nested Expected Value that Aren't Independent

I'd like to mention this is a homework problem and I am interested in the process of finding the answer, not the answer itself. The problem is, we have: A random variable X uniformly distributed on ...
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1answer
280 views

Using the MSE criterion, which is a better estimator for $\Theta^2$?

Question: Let $T_1$ and $T_2$ be independent unbiased estimators of a parameter $\Theta$. Assume that $\operatorname{Var}(T_2) = \operatorname{Var}(T_1)$. Using the MSE critertion, define which is a ...
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1answer
99 views

Finding $E(\bar{X^2}|\bar{X})$ [duplicate]

Possible Duplicate: Finding $E\Bigl(\overline{Y^2}\Bigm|\overline{Y\vphantom{Y^2}}\Bigr)$ by Basu's theorem? Suppose $X_1,\ldots,X_n$ are a random sample of $N(\theta,1)$. if ...
2
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1answer
202 views

Needing to find a variance from a data set below

I am trying to get the variance of the data set below. I get a negative number upon applying 1/2(2.5)^2 + 1(3)^2 + 0.5(4.5)^2 + 1(5)^2 + 1(6)^2 - (17.5)^2 = variance, but a negative and weird number. ...
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2answers
70 views

Closing 3 numbers

I have 3 numbers that physically must add up to zero. Unfortunately, each is obtained from a noisy measurement and they don't add up exactly. Assuming the noise is Gaussian and given 3 corresponding ...
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2answers
2k views

Probability/Combinatorics Problem. A closet containing n pairs of shoes.

A closet contains n pairs of shoes. If 2r shoes are chosen at random, (where 2r < n), what is the probability that the chosen shoes will contain no matching pair? I have tried thinking about this ...