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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Let X_1,..,X_n i.i.d negative binomial. Find the best unbiased estimator for P(x<=3)

I am not sure where I should even start with this problems. I know that the sum of negative binomial random variables is itself a negative binomial random variable. I am sure that I can show that the ...
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0answers
2 views

For X,Y symmetric zero-mean random variables, does $V(X)\geq V(Y) \Rightarrow E(|X|)\geq E(|Y|)$?

I need to show the following thing. Consider two continuous random variables $X,Y$ which take values in $[-1,1]$ and are both symmetric around zero. How can I show that $V(X)\geq V(Y) \Rightarrow ...
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0answers
16 views

Tricky Poisson Distribution question

Given that $N~Po(\lambda t)$, where N is the number of customers arrived. Find the probability that, after t minutes, fewer than 2 customers have arrived. The above question requires $Pr(N<2)$ ...
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1answer
17 views

How to interpret p-value in this problem.

The following is the question in particular, I got this question wrong. However nothing I run across explains why it is wrong. I answered C because with a p-value of 0.087 we don't have an "unusual" ...
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0answers
5 views

solution for statistics [on hold]

An agriculture researcher samples 25 mandarin trees to study the average number of fruits per tree. If the sample mean is 825 with the standard deviation of 150. The 98% confidence interval for the ...
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31 views

Negative exponential distribution to the poisson distribution

In this question I have found the pdf of $T_1$ and $W_2$. For part (f) i just multiplied the pdf of $T_1$ and $W_2$ and substituted: $w_2 = t_2 - t_1$ and finally got: $f(t_1,w_2) = \lambda^2 ...
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1answer
16 views

Find constant given two random variables and pdf [on hold]

Any idea how i can find K given two random variables X,Y
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1answer
25 views

How can you find $P(\frac{X}{Y-X}<0)$ if $X\sim Geometric(p)$ and $Y\sim Bernoulli(p)$

Let the independent random variables $X\sim Geometric(p)$ and $Y\sim Bernoulli(p)$, I want to prove that $P(\dfrac{X}{Y-X}<0)=(p-1)^{2}(p+1)$. Do I need the joint probability mass function for ...
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0answers
15 views

Statistic Help please … [on hold]

Find the minimum sample size needed to estimate the mean price of a certain model of Tv at a 95% confidence level if the margin error is \$122 and sigma is known to be \$553 a) 69 b)79 c)78 d)70 ...
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1answer
15 views

Can this be a covariance matrix

$$\begin{bmatrix}10& 3& 1\\ 2& 5& 0\\ 1& 0& 2\end{bmatrix}$$ $$\begin{bmatrix}2& -4& 0\\ -4& 3 &1\\ 0& 1& 2\end{bmatrix}$$ I know that ...
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3answers
19 views

Does the negative distribute? interpreting notation

so this is sort of a silly question but I want to be clear of the meaning of this for generalization purposes. This is concerning Z scores, where $\Phi(x)$ = the (c.d.f) of a standard normal ...
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0answers
16 views

Automatic derivation of sample variance [on hold]

Given a formula that uses a sample to retrieve information, is there a way to automatically derive it's error (as variance?). For example, in two-stage sampling there is a variance formula given that ...
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1answer
31 views

You toss two six-sided dice [on hold]

A. Find the probability of getting a one on the first die and a four on the second die. B. Find the probability that both dice show an even number.
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1answer
16 views

Which type of correlation should I use?

I am beginner in statistics. I have excel table with few columns. I would like to find correlation between the variables. I have to make an essay to my boss and he wants concrete answers. I searchin ...
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1answer
24 views

Spearman's correlation between two variables, when one is a linear function of the other

According to Spearman's rank correlation (denoted henceforth as $\rho$), given two variables $X,Y$, when each of them is a perfect monotone function of the other, we should expect it to be either $1$ ...
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0answers
8 views

R^2 in Generalized Linear Models

I am trying to model relationship between predictors and explained variable in R using glm() function. I've found quite good model that gives me satisfactory results. Is there some way how to ...
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0answers
7 views

Generalised additive models

I fit an generalised additive model to my dat set using R. And found that the effective degrees of freedom for one of my dependent variables was 7.732 . However I'm not sure what this suggests about ...
2
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1answer
30 views

Set of pairs of options that could be wrong/right

One has a list of n options out of which 2 are incorrect, and guesses can be made by picking a pair of options. After picking a pair as a guess, it is either valid, in which case both of the pair's ...
2
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1answer
14 views

Expected loss in regards to a question containing a continuous random variable with uniform distribution

I have a general question about a homework assignment that deals with a uniform distribution of a continuous variable. Here is the question (and the parts of the question): Suppose parking rules are ...
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0answers
22 views

Which is the best method/algorithm to predict rank in an exam based on historical data?

I have the 10 year historical data(mark and rank) of all students who took an exam (exam happens once in an year and the patter of the exam is always same(number of questions and marks per question) . ...
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1answer
34 views

Pascal's triangle

I was out sick for a while (2 weeks) and just got back and now we are doing whatever this is! Can someone explain to me what this is or show me a video on how to do it? "Use Pascal's triangle and the ...
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2answers
28 views

Correlation Coefficient of data on $y = mx + b$ [on hold]

Suppose n cases of data on $x$ and $y$ fall exactly on the line $y = mx + b$. Compute the value of $r$. (Hint: In any of the formulas for $r$, eliminate all $y$ in favor of $x$.)
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1answer
20 views

Chance of Winning Sale [on hold]

If there is a 25% chance of winning a sale but I suck at selling so my chances of making this sale is 20%, what is my probability of winning this particular sale?
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38 views

EV of sequences of coin flips

I have a biased coin $C$ where $P(H) = p$ and $P(T) = 1-p$. This coin could be tossed an infinite number of times and the results will be recorded. I want to calculate the probability of a given ...
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2answers
23 views

when tossing a coin ten times, what is the probability of an outcome which has a string of 3 or more heads as well as a string of 3 or more tails?

here is an experiment from my Stat textbook "Try this experiment: Write down a sequence of heads and tails that you think imitates 10 tosses of a balanced coin. How long was the longest string ...
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2answers
30 views

Frequency of the most frequent word using Zipf's law

I modeled my corpus using Zipf's law, so that: $$f_r=c/r$$ Where $f_r$ is the frequency of a word at rank $r$. I calculated $c=90000$. How can I calculate the frequency and the occurrence for the ...
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0answers
102 views

Help to understand the Monty Hall Problem [on hold]

I have read the Monty Hall Problem and explanations on Wikipedia several times and fail to grasp how exactly 'conditional probability' is being realistically applied. More specifically, my logical ...
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0answers
12 views

Generalized least squares equation project [on hold]

I am trying to come up with a project incorporating the generalized least squares equation. Does anyone have any ideas of what I could do or where I may be able to find data for this particular ...
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0answers
15 views

Help simplifying equation (sample variance is an unbiased estimator)

I would like to know how you get from this to $\sigma^2$. I tried to simply as much as I could and got
3
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1answer
32 views

UMVUE of $ \frac{1}{\theta} $ coming from $ f(x) = \theta x^{\theta - 1} $.

Let $ X_1,\ldots,X_n $ be i.i.d. sampled from the distribution $$ f(x;\theta) = \theta x^{\theta - 1}, $$ where $ x \in (0,1) $ and $ \theta > 0 $. Show that $$ T(x_{1},\ldots,x_{n}) = - ...
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0answers
32 views

Probability and stats question [on hold]

Im kinda confused on how to approach this question and how to solve for it. i know there are multiple ways but i was wondering if anyone could help me. thanks 1.) It appears that the mean commuting ...
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1answer
21 views

Understanding two sided t-test

Assume we have two search engines, A and B. I get a list of scores for 10 different queries. Now, I model this with a t-test in order to test significance. These are my hypothesis: $H_0: B-A=0$ ...
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0answers
12 views

How to estimate theta by method of moment estimator and determine maximum likelihood estimators

I have not learnt the POINT ESTIMATION but I have had time to go through some written notes on how to estimate theta1 and theta2. I would love to do this question but I am lacking some knowledge on ...
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2answers
33 views

Finding average using central limit theorem.

I'm have a lot of trouble trying to wrap my head around how exactly to use the central limit theorem in this question. Image a gambling casino consisting of 100 busy roulette tables. Suppose that ...
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1answer
26 views

Fifty men and thirty woman are lined up at random. How do I find the expected number of men who have a woman standing next to them.

Fi.fty men and thirty woman are lined up at random. How do I find the expected number of men who have a woman standing next to them.
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1answer
18 views

How would one estimate the number of commercial airplanes bought in the US every year? [on hold]

I am not sure where to start with this question. Do you start by estimating number of major airports? How many airplanes decommissioned/and new ones bought?
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1answer
26 views

What is the expected value of the highest of N independent draws from the unit uniform distribution?

I have a seemingly innocuous problem that I can't seem to wrap my head around. The following is mentioned in passing on one of my lecture slides, but when I try to arrive at the same conclusion I get ...
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2answers
27 views

How do the statistical calculation according to X people? [on hold]

It's common to read something like "for 10 people, 5 prefer something" (5 people this total of 10 people).Eg: 8 in 10 people over 50 years old use the Internet ...
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0answers
35 views

Help: Studying A-Level Mathematics [on hold]

Although I am a latecomer at the age of 21 years of age, I have enrolled in self taught mathematics A-level with "Edexcel" both mathematics & further mathematics. I am in need of help with ...
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0answers
22 views

Product of (multivariate) Gaussian densities

One can frequently read that the product of two multivariate Gaussian pdf f1(x) and f2(x) is itself a Gaussian, with parameters as defined for example in: ...
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0answers
10 views

Xi~Poi(theta) and let Tau(theta)=e^theta. a) find the MLE of Tau(theta). [on hold]

consider a random sample from a poisson distribution, Xi~Poi(theta) and let Tau(theta)=e^theta. a) find the MLE of Tau(theta). b) Is this MLE an unbiased estimator of Tau(theta) c) Find the CRLB ...
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1answer
11 views

Normal Distribution: Statistics

I'm having a lot of trouble trying to remember the formulas on how to calculate these questions. Any help would be great. An automobile insurer has found that repair claims are Normally distributed ...
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1answer
17 views

Prove that a symmetric distribution has zero skewness

Prove that a symmetric distribution has zero skewness. Okay so the question states : First prove that a distribution symmetric about a point a, has mean a. I found an answer on how to prove this ...
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0answers
17 views

Random Variables and Statistic

I'm studying Statistical Inference by Casella and I'm confused with the definitions of random variable & statistic. So let we have the probability space $(\Omega, F, P)$ where $\Omega$ is the ...
0
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2answers
20 views

Expectation of a discrete variable [on hold]

Suppose $P(X=n)=kq^{n-1}$ where k is a constant. Then how do I find a value for the expectation of X?
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0answers
15 views

Find upper bound of probability value using Chebyshev's inequality [on hold]

Given density function of random variabel X is f(x) = 1/(2√x), for -√3 < x < √3. Use Chebyshev's inequality to find upper bound of probability value P(IxI≥3/2).
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1answer
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Find lower bound of probability value using Chebyshev's inequality

Given density function of random variabel $X$ is $f(x) = 3x^2$, for $0 \lt x \lt 1$. Use Chebyshev's inequality to find lower bound of probability value : $P(5/8 \lt x \lt 7/8)$ $P(1/2 \lt x \lt 1)$ ...
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1answer
11 views

Find the probability P(x is even) of given cumulative distributive function [on hold]

Given cumulative distributive function (CDF) $F(x) = 1 - (1/2)^{(x+1)}$ for $x = 0, 1, 2, ...$ Find the probability value P(x is even).
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0answers
20 views

expectation calculation problem small problem

a Continuous, positive random variable X, whose PDF is proportional to $(1+x)^{-4}$, where $0<x<\infty$, determine $E(X)$ i tried to solve it directly by integrating from 0 to infinity to get ...
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0answers
14 views

Bayesian update multivariate normal based on one-dimensional signal: simple rule

Is there a simple rule to update the linear combination of normal distributions based on a one-dimensional signal? The unconditional joint density of $(\eta,\theta)$ is multivariate normal ...