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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Probability Question

The credit department of a clothing shop reported that 30% of their sales are through cash/check, 30% are through credit card and 40% are through debit card. 20% of the cash/check purchases, 90% of ...
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Does the central limit theorem state that if $Y_i$ is i.i.d. and *n* is sufficiently large then we can assume that $Y_i$ is normally distributed?

Does the central limit theorem state that if $Y_i$ is i. i. d. and n is sufficiently large then we can assume that $Y_i$ is normally distributed?
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Median for continuous distribution

Consider a continuous random variable X with probability density function given by $f(x)=cx$ for $1 \le x \le 5$, zero otherwise. Find the median. First I calculate the CDF: $F(x)=cx^2/2$ for ...
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65 views

Proving a random variable

Here is another question from the book of V. Rohatgi and A. Saleh. I would like to ask help again. Here it goes: Let $\mathcal{A}$ be a class of subsets of $\mathbb{R}$ which generates $\mathcal{B}$. ...
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47 views

What is Bayesian Evidence?

Could someone explain this concept or give a link to the explanation of this concept please? I know what "Bayesian" is, but I don't know what "Bayesian evidence" is. A good explanation of "evidence" ...
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Let (X,Y) have a Dirichlet Distribution with paramters $(\alpha_1, \alpha_2, \alpha_3)$ Establish that X~Beta$(\alpha_1, \alpha_2 + \alpha_3)$

If the joint pdf of (X,Y) is $f(x,y)=\frac{\Gamma(\alpha_1 + \alpha_2 + \alpha_3)}{\Gamma(\alpha_1) \Gamma(\alpha_2) \Gamma(\alpha_3)} x^{\alpha_1 - 1} y^{\alpha_2 - 1} (1-x-y)^{\alpha_3 -1}$ ...
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Median for Continuous Probability Distribution

Consider a continuous random variable X with probability density function given by: $f(x)=4x(1-x^2)$ for $0 \le x \le 1$ Find the median. So to calculate the median, I calculated the ...
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41 views

matrix spectral representation

can you give me any idea how to show this? Show that $A \ge I$ implies $A^{-1} \le I$, and use this result to deduce that $A\ge B\ge0$ implies $0\le A^{-1} \le B^{-1}$. I think this question is ...
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1answer
30 views

Probability of a combination

If you have 6 red marbles and 6 blue marbles and 1 white marble, what is the probability of any combination granted it has always has a white marble in a combination of 6 random drawn marble? If you ...
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90 views

What is the probability there are two or more claims?

In a group of policy holders for house insurance,the average number of claims per $100$ policies per year is $\lambda=8.0$. The number of claims for an individual policy holder is assumed to follow a ...
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45 views

Statistics of Lists

To start, let me say i am a programmer and not a math wiz, so this question might be very simple. I have a data set of prices that sort of looks like this ...
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254 views

How to find the probability there are 11 or more cars?

During rush hour the number of cars passing through a particular intersection has a Poisson distribution with an average of 540 per hour. Find the probability there are 11 or more cars? The answer is ...
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21 views

algorithm for generating interesting normal symmetric continuous functions

Does any one know of, or can think of an algorithm which generates arbitrarily many symmetric normally distributed continuous functions? And when I say interesting I mean more complex distributions ...
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55 views

Multiple regression and hypothesis test $H_0$:$\beta_2=0$

Multiple regression model $H_0$:$\beta_2=0$, $H_1$:$\beta_2 \neq 0$ where $\beta_2$ is the vector of elements ($\beta_2, \beta_3, \dots, \beta_k$) and $\beta$ is slope of regression line. Why it is ...
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144 views

Searching for random items in a set of lists

This is a programming question, but I'm interested in the math behind it so I think it's better asked here. Say I have a list of items and I'm looking for one item in the list that satisfies a ...
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173 views

Why is Wolfram giving me a different answer for standard deviation?

I have the following set of data: ...
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98 views

Adaptation of sum of arrival times of Poisson process

Let $\{N_t\}_{t\geq0}$ be a Poisson process and $\{F_t\}_{t\geq0}$ be its nautral filtration so that $\{N_t\}_{t\geq0}$ is adapted. $T_i$ be the $i$th arrival time of Poisson process of arrival rate ...
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282 views

Geometric Mean of an Interval

Is there any way to calculate one? If it't not clear what I mean, here's an example: Starting with an initial value, keep multiplying it by some random amount on the interval [1, 2] at regular ...
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82 views

Probability when flipping a coin

A warped coin has probability of 0.5 of landing Heads, probability of 0.4 of landing Tails, and probability 0.1 of landing on its Edge. It is flipped 5 times. What is the probability that more Heads ...
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41 views

Sampling and normal distributions

There's a criteria used in my book which describes that $\hat{p}$ is approximately normal provided that $npq \geq 10$. Where did this assumption come from? $n$ is the sample size, $\hat{p} = ...
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23 views

Deriving Statistical quantites from other quantities

Studying for a statistics exam and I am stumped on the following: For a set of sample data, the following values were found. Fill in missing values Variable: X N: ? Mean: ? SE Mean: 2.05 StDev = ...
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162 views

The MLE of a $N(\theta, 1)$ distribution

I am trying to find the Maximum Likelihood Estimator of an i.i.d. sample $X_1, \ldots, X_n$ arising from the model $N(\theta, 1)$, where $\theta \in [0,\infty)$. I have done this problem previously ...
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95 views

Hypothesis testing with poisson distribution

At a nuclear plant great care is taken to measure the employees health.These are the number of visits made by each of the 10 employees to the doctor during a calender year. 3,6,5,7,4,2,3,5,1,4 ...
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48 views

An example where $E[X_1 X_2] - E[X_1]E[X_2] = 0$ for functions $X_1$ and $X_2$

I computed $E[X_1 X_2] - E[X_1]E[X_2]$ using $X_1 = 3x+1$ and $X_2 = 2x+5$ the following way: $E[(3x+1)(2x+5)] - E[3x+1]E[2x+5] = E[6x^2 + 17x + 5] - (3E[x]+1)(2E[x]+5) = 6(E[x^2] - E^2[x]) = ...
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265 views

Finding a marginal PDF of a joint probability distribution

I understand the idea of how to do it, but I'm currently getting a constant as my marginal PDF, which doesn't make sense. The overall distribution is as follows: $f(x,y) = 5ye^{-xy}$ for $0 < x, ...
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52 views

Elevated percentage of standard BMI associated with Carcinoma

Percentage of Standard BMI$\hspace{30mm}$Male$\hspace{40mm}$Female $\hspace{70mm}$Case$\hspace{10mm}$Control$\hspace{20mm}$Case$\hspace{10mm}$Control ...
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53 views

help find my error in a statistics transformation computation

This is a low-priority question, but it has been bugging me so I thought I'd ask. In my stats homework I have the following exercise: Exercise. Suppose $X_1$ and $X_2$ are iid observations from the ...
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222 views

Help needed…Statistics probability and z table…stuck

The question is: **An estimated 1.8 million students take on student loans to pay ever-rising tuition and room and board (New York Times, April 17, 2009). It is also known that the average cumulative ...
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67 views

How to write this conversion algorithm

I have to calculate Grade Average from the scale of 1 to 5 such that 1 being the best (100%) and 5 being the worst (0%). So we have, ...
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124 views

meaning of math symbol in probability expression?

anyone knows the meaning of the marked symbol in the pic and its Latex syntax?
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43 views

Calculating sample size

A city Humane Society wishes to determine the life expectancy of adopted dogs from their shelter. How many of the dog owners do they need to contact in order to be 90% confident of being within 0.29 ...
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61 views

Redundancies in covariance matrix

We know that covariance matrix is symmetrical. I have a vague intuition that there may be some other redundancies beyond that. For example, if A is correlated to B and B is correlated to C then A and ...
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433 views

Continuous random variable with density function

$X$ is a continuous random variable with p.d.f. $f(x) = c\space e^{-x} ; x > 1$. Find $P(X < 3|X > 2)$
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34 views

Contingency table on Bayers Rule

The question is this: A medical test for the disease StatsLove will correctly state that a diseased student suffers from StatsLove 95% of the time. The medical test correctly states that a ...
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1answer
371 views

Stuck…please help to understand how formula works in order to Find the standard deviation in normal distributions

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has ...
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170 views

Find the value of theta.

Let $X$ have the density function $f(x) = \dfrac{3x^2}{\theta^3}$ for $0 < x < \theta$, and $f(x) = 0$ otherwise. If $P\{X > 1\} = 7/8$, find the value of $\theta$. I don't know
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Let $X$ be a discrete random variable with probability function $P(X=x)=\frac2{3^x}$ for $x = 1,2,3,\ldots$ What is the probability that $X$ is even?

Let $X$ be a discrete random variable with probability function $P(X=x) = \frac{2}{3^x}$ for $x = 1,2,3,\ldots$ What is the probability that $X$ is even? I have: ...
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574 views

Let X be a continuous non-negative random variable with density function f, and let Y = X^n. Find the probability density function of Y

Let $X$ be a continuous non-negative random variable with density function $f$, and let $Y = X^n$. Find the probability density function of $Y$ I have: $$F_y(y)=P(X^n\le y)$$ if $y<0$, then ...
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341 views

statistcs z-table standard deviation question…Please help.

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has ...
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1answer
3k views

Derivation of formula for finding median for grouped data

I know the formula of formula for finding median for grouped data that is $$\mathrm{Median} = L_m + \left [ \frac { \frac{n}{2} - F_{m-1} }{f_m} \right ] \times c$$ and I know what all the letters ...
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38 views

How many 7-character passwords can be generated with…Stipulations?

Characters can only be (a-z), (A-Z), and (0-9) w/stipulation that first character must be a lower case letter, the last character must be an upper case letter, and of the 5-characters in the middle ...
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1answer
243 views

Why use Euclidean distance in linear model?

The method of least squares is the most basic method in statistical linear models. For the simplest linear model$$Y_i=\beta_0+X_i\beta_1+\epsilon_i$$we are looking for $\beta_0$ and $\beta_1$ that ...
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1answer
53 views

Sample Variance Part B)

The random variable $$ S^2=\sum_{i=1}^n \frac{(X_i- \overline X)^2}{(n-1)} $$ is called the sample variance. A) Show that $ (n-1)S^2=\left[\sum_{i-1}^n ((X_i-\mu)^2 \right]-n(\overline X-\mu)^2 $ ...
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68 views

simultaneous probability elicitation from multiple agents without an exogenous banker

A proper scoring rule is a function $f:[0,1]\times\{0,1\}\to \Bbb R$ such that, if a subject will receive a reward of $f(x,0)$ for reporting his estimate of the likelihood of an event as $x$ if the ...
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106 views

Sample Variance question

The random variable $$ S^2=\sum_{i=1}^n \frac{(X_i- \overline X)^2}{(n-1)} $$ is called the sample variance. A) Show that $ (n-1)S^2=\left[\sum_{i-1}^n ((X_i-\mu)^2 \right]-n(\overline X-\mu)^2 $ ...
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3k views

How do you calculate an upper-confidence bound on a problem with 2 means?

I am presented with: Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be σ1 = 0.10 and σ2 = 0.15 fluid ounces for ...
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57 views

What on earth is (B|A)?

I'm stumped and getting nowhere with this question: Description: The Air Pollution and Mortality data of 60 cities were collected in a study. 11 can be considered to have high hydrocarbon pollution ...
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40 views

Find the probability one of a sample is less than a value

I'm having trouble trying to solve this question, the context is pH acidity in rain: mean = 3.719 sd = 0.546 You are given that the probability that a rainfall collection has a pH less than 3.2 is ...
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275 views

Probability & Statistic on point estimate

May i know how do I calculate a point estimate of the values that separates the largest 10% of all values in the thickness distribution form the remaining 90%
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139 views

The probability that a randomly chosen grain weighs less than the mean grain weight

If Y has a log-normal distribution with parameters $\mu$ and $\sigma^2$, it can be shown that $E(Y)=e^\frac{\mu + \sigma^2}{2}$ and $V(Y)=e^{2\mu +\sigma^2}(e^{\sigma^2}-1)$. The grains composing ...