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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Substituting observations for functions of random variables

I am not sure if this question makes sense, but I would like to seek clarification as it has been bothering me for sometime. In statistics I see theories being developed for random variables. For ...
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1answer
162 views

What are the chances of winning with a specific card in Spades

In the game of spades, a standard deck is shuffled then all the cards are dealt in a clockwise manner until each of the 4 players has 13 cards. The first play of the game is for each player to throw ...
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63 views

Financial mathematic with Feynman-Kac

I have a really big task in financial mathematics and a small part of it (to set up the problem), I need to write a PIDE (the Feynman-kac) where we estimate options with jumps. It is derived from the ...
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1answer
122 views

Central Limit Theorem: asymptotic distribution

I keep reading in the documents about the asymptotic distribution of the CLT. I am learning things by myself so try to figure it out on my own and don't have a teacher to ask the question to. So it's ...
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1answer
31 views

what “average” to use that will give the most relevant value f0r portfolio

My assignment requires me to find return on capital, industry wise for the loan portfolio classified into various industry/sector, the data fields are : ... Name of account|industry|Outstanding ...
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1answer
64 views

Grade 9th middle school question

the mean of 5 apple is $12$, the range of the biggest and the lowest is $6$. If every apple is subtracted by $a$ then the sum is divided by $b$, the new mean is $2$ and the range of the biggest and ...
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105 views

Central Limit Theorem Clarification

The Central Limit Theorem states that the sampling distribution of the sample mean: Converges in distribution to a normal distribution. Has an expected value (mean of the sampling distribution of ...
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1answer
92 views

Hypothesis test question

Can anyone check my answer about hypothesis test? Thanks!
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1answer
97 views

The joint pdf of the amount X of almonds and amount Y of cashews in a 1-lb can of nuts

The joint pdf of the amount $X$ of almonds and amount $Y$ of cashews in a 1-lb can of nuts was: $f(x, y) = \begin{cases} 24xy & 0 \leq x \leq 1,\, 0 \leq y \leq 1,\, x + y \leq 1\\ 0 & ...
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1answer
109 views

Random variable X has the following discrete distribution

Random variable $X$ has the following discrete distribution: $f(x) = k/x$ for $x = 1, 2, 3$ $f(x) = 0$ otherwise Find $k$ so that $f(x)$ is a legitimate probability mass function What is ...
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60 views

Can anyone check my answers?

This is about hypothesis testing. Please check my answers Thanks!
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2answers
265 views

How can I show rank $( AB)$ = rank $( A)$?

Can you help me how to show rank $( AB)$ = rank $( A)$ iff null$(A)$ $\cap $ range$(B) = \{0\} $? I can understand that rank $(AB)$ would be no greater than rank A. But not sure how to show this ...
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1answer
41 views

Can I get weighted sample variance from the individual variances?

Suppose I have daily aggregates: mean ($m_i$), variance ($v_i$) and number of samples ($n_i$); and I want to calculate weekly aggregates from these. Weekly mean, $M$, is simple: its just a weighted ...
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1answer
87 views

Variance for mixed distribution (continuous + discrete)

A random variable X has the cumulative distribution function: $F(x)= \left\{ \begin{array}{l} 0 \text{ for x < 1}\\ \cfrac{x^2-2x+2}{2} \text{ for } 1 \le x <2\\ 1 \text{ for } x \ge ...
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1answer
41 views

Relation of parameters of fitting lines

Scientists want to find the relation between two variables $x$ and $y$ by line $$y=ax+b.$$ After some experiments, scientist $S_i$ find the best parameters are $(a_i, b_i)$. It is sure that ...
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9 views

Certifying filtered data

I have a set of data. I have filtered using FFT. My question is the folowing: How to show, statistically, that the filtered data came from the initial set of data.
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44 views

How can I determine this equation?

I have an equation that have been formulated as: $$\Delta w_{ki}=\eta (y_{k}-y_{o})(x_i-x_o)+a_1,$$ where$$y_{k}=\sum_{j}w_{kj}x_{j}+a_{2}$$ and where $a_1,\eta,x_o ,y_o$ and $a_2$ are constants and ...
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1answer
81 views

Finding meaningful differences in a set of time measures

An individual is presented with a list of words, one at a time, and asked to answer the first thing to comes to her mind. The delay of all answers is recorded. So I have a list of words, each paired ...
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1answer
57 views

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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1answer
19 views

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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22 views

How to extract projected points from Factor Analysis?

I am currently comparing different projection methods to derive 2D screen coordinates from high-dimensional point clouds. This is often done with PCA, MDS, LLE, SNE, etc. and I want to compare them ...
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2answers
101 views

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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2answers
62 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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1answer
28 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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1answer
74 views

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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478 views

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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1answer
33 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
21 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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1answer
45 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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32 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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3answers
76 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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17 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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63 views

Delta Method : Ambiguity in the proof by K. Knight

I am posting this message because I read the proof of the Delta Method (theorem 3.4) in K. KNIGHT, Mathematical Statistics, Chapman \& Hall CRC, 2000, p120-121. and there is something that ...
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46 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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1answer
94 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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1answer
107 views

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

I have the following set of data: ...
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1answer
1k views

Find probability when drawing marbles

Two marbles are drawn randomly one after the other without replacement from a jar that contains 8 red marbles, 8 white marbles, and 8 yellow marbles. Find the probability of the following events. ...
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81 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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1answer
59 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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1answer
62 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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127 views

Binomial Distribution and Probability - Statistics

A study concerning the relative influence of husbands and wives in consumer purchasing, which appeared in recent issue of Time Magazine, reported that husband exerts the primary influence in selecting ...
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1answer
36 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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1answer
16 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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32 views

calculate probability using recurrence relation of poisson distribution

if P(x=2)=0.00227 and P(x=4)=0.01817 then calculate P(x=1),P(x=3) and P(x=5) by using recurrence relation of poisson distribution
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1answer
78 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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61 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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42 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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15 views

What statistical analysis to use to separate abnormal group(s)?

Assume I am a headmaster of a school and have ONLY 6 students (LOL, a small school). Each student is taken care by a teacher (6 teachers total). Now I want to analysis the teacher performance based on ...
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1answer
149 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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2answers
40 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 ...