A probability provides a quantitative description of the likely occurrence of a particular event.

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Dirichlet distribution: Normalization of alpha values

I'm a programmer and currently trying to apply the Latent Dirichlet Allocation algorithm by Blei et al. on a text mining problem. I am using a library called gensim for this, which takes, among ...
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2answers
73 views

How to prove dependence of random variables

I need to solve the following problem. Let $X$ be a normal random variable with mean $\mu$ and standard deviation $\sigma$ and let $I$, independent of $X$, be such that $\mathbb{P}(I = 2) = ...
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5 views

How to estimate parameters for a general compound distrubtion

I have am acquiring data drawn from a compound distribution of the form $$ f(x; \sigma, \mu, \sigma_{\mu}, \sigma_{\sigma}) = \int_{\hat{\mu} \in R_1} \int_{\hat{\sigma} \in R_2} p(x; \hat{\sigma}, ...
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46 views

Finding the sample space of an experiment

Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age. List the sample ...
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0answers
9 views

Statistically detecting different sampling distributions with summary statistics [on hold]

Suppose to I have two different possible distributions: Distribution $A$ is a set of $N$ Gaussian random variables, each with their own mean $\mu_i$ (normally distributed with mean $\mu$ and variance ...
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19 views

Probability question- From Mathematica program

Could somebody please help me, I have been trying to calculate this problem all day, but with no success. Here is the problem: "A teacher was asked by her principal to select 7 students at random ...
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1answer
32 views

Variance of product of two random variables

I’m trying to calculate the variance of a function of two discrete independent functions. The first function, “f(x)”, returns a value of 0 with probability 0.243, a value of 1 with probability 0.306, ...
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12 views

Size and Power of Test: Poisson Distribution

In a homework problem, I am given a Poisson distribution with lambda = 1 as null hypothesis, lambda greater than or equal to 2 as an alternate hypothesis, and 3 as a test statistic. I am instructed to ...
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27 views

Binomial Probability (Dice)

The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of the throws with 0, 1, 2,..., 6 successes are summed over all six pairs are as ...
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1answer
22 views

Pointers on calculating probability/odds from data vectors

I am trying to figure out how to calculate probability and odds for the variable Target. ...
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7 views

What are the right values for the prior mean and prior variance matrix in choice design?

I am doing my first choice experiment with JMP & the tutorial I found at http://blogs.sas.com/content/jmp/2009/01/15/optimal-design-of-the-choice-experiment/ Right now I am not sure if I ...
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5 views

What are fitted coefficients in magnitude in choice experiments?

I am new to choice experiments and trying to learn the mandatory basics. One reference I am using is the page http://blogs.sas.com/content/jmp/2009/01/15/optimal-design-of-the-choice-experiment/ I ...
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69 views

Problem obtaining a marginal from the joint distribution

Suppose $X_1$ and $X_2$ have the joint pdf $$f_{X_1,X_2}\left(x_1,x_2 \right)=4x_1 x_2,\quad\text{for}\quad 0<x_1<1, 0<x_2<1$$ From that I found the joint pdf of $Y_1=\frac{X_1}{X_2}$ ...
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0answers
10 views

How to calculate the distribution of spend on options of a new car

I have a bit of a real world conundrum and I have reached the limited of my knowledge. The problem in question relates the distribution of the amount of money spent on options when buying a new car. ...
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1answer
24 views

Probability in choice experiments

I just started to get into the theory of probability/choice experiments and there are some topics that I don't understand. Hope you can help me to get the hang of it. Lets say the following ...
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2answers
21 views

Need help finding the probability

I have problem where you are given the number of times you must win, and the chance of winning a game. I need to find the probability that I win all 4 times. Example: I am only given two inputs, 4 ...
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2answers
26 views

Calculating upper and lower bounds of the probability of outcome i occuring?

Let's say we observe a sample choosing between three possible outcomes: a, b, and c. We can then easily calculate the probability of an individual choosing outcome a: # people choosing a / total # ...
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36 views

Probability of disease given multiple samples of a single test

Someone either has disease X or they are healthy. A test is used which is 90% sensitive and 80% specific (81.81% precise). The test is performed 8 times with different samples from the same person. ...
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18 views

Distribution of noninjective function of random variables

Let $(X,Y)$ is a bivariate normal random variable wit mean $(0,0)$ and covariance matrix $\Sigma.$ Suppose that $T:\mathbb R^2\mapsto\mathbb R.$ I wish to compute the distribution of $T(X,Y).$ How ...
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16 views

Normal distribution probabilities [on hold]

Suppose that one out of every ten plasma televisions shipped has a defective speaker. Out of a shipment of n=400 televisions, find the probability that there are: a. at most 40 with defective ...
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0answers
10 views

Probability of two identical names (given + surname) belonging to two different persons

I have two datasets. In each datasets, observations are assigned to individuals identified by a variable name (constituted by given name - or proper noun - and ...
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32 views

Elegant way to plot a probability density function?

Given a set of samples I would like to draw a nice plot showing their probability. Something like this (notice the vertical bar showing the samples): Or even harder like this (considering a weight ...
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1answer
50 views

Convolution of random vectors

Suppose, I have two random vectors $A=[A_1, A_2, \dots A_k]$ and $B=[B_1, B_2, \dots B_m]$. What could be the joint PDF $f_{\mathbf{y}}(y_1,y_2,\dots y_N)$ where $\mathbf{y}=A \ast B$, here $\ast$ ...
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0answers
31 views

Where to start to learn about pricing models?

I have a situation at my work that I want to take as a chance to learn more about pricing and stats. In a nutshell, I work for a company that buys several products and then charges a margin (we have ...
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37 views

sum of $n$ independent F distributed random variables

I need a help: What will be the distribution of sum of $n$ independent F distributed random variables with parameters 1 and 1 (i.e., $F(x;1,1)$? Great if you can suggest some references too, Thanks ...
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1answer
104 views

How to apply Bayes' theorem to the search for a fisherman lost at sea

The article The Odds, Continually Updated mentions the story of a Long Island fisherman who literally owes his life to Bayesian Statistics. Here's the short version: There are two fishermen on a ...
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44 views

Probability of $P(X_1<X_2|X_1<2X_2)$ and $ \ P(X_1<X_2<X_3|X_1<1)$ [closed]

Find the $P(X_1<X_2|X_1<2X_2)$ and $ \ P(X_1<X_2<X_3|X_1<1)$ Given: $f(x) = e^{-x}, \,\,\, 0<x<\infty,\,\,\,$ zero elsewhere. The rvs have same pdf and they are independent ...
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12 views

Expected number of clusters of points within a given distance

I have a set of N uniformly distributed points in a square whose dimensions are known. I need to find the expected number of clusters we are going to form. We will form clusters based on a region ...
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13 views

Cluster Sampling problem

I'm using Sharon Lohr's book to self-study, and there is no solution to this problem. I just wanted to make sure I'm computing the values correctly. Question: The new candy Green Globules is being ...
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1answer
66 views

Convergence of Random Sequence

I have a two statements. One says: $$-\frac{1}{T} \sum_{t=1}^T X_t \rightarrow a $$ in probability as $T \rightarrow \infty$. The other: $$-\frac{1}{g(T)} \sum_{t=1}^{g(T)} X_t \rightarrow a $$ in ...
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30 views

What does a linear/geometric probability in time series mean?

In some discrete time series I analyzed I'd like to interpret whether there is a meaning to the observed probability model. The data is some discrete time series with a population of objects which at ...
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1answer
45 views

Probability to Likelihood

I have a problem on calculating the likelihood of observing a data point x given the predicted lable. My application is on text classification where I have to detect Spam and No Spam documents. I ...
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10 views

Want to findout satistical distance unsing another procedure except kullback liebler divergence

i want to find the distance between two pdf(pdf is calculated using kernel density estimator from two random data set of different size ) .Is there any alternative and efficent way to calculate ...
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0answers
30 views

calculating Std deviation based on sample size and proportion and the probability [closed]

I need to know how to calculate the standard deviation using the sample size and proportion, for example from a survey of 161 people by a phone company its established that .68 will switch provider at ...
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2answers
73 views

basic probability problem

Problem 2 (page 33 of text) Assume that every patient with a particular type of disease has the probability 0.1 of being cured within a week, if the patient is given no treatment for the disease. Ten ...
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1answer
61 views

Tossing 2 coins, distribution

We are tossing 2 fair coins once. Then for the next toss we are only tossing the coin(s) that came up heads before. Let $X$ be the total number of heads. The question is $EX$ and the distribution ...
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1answer
62 views

What would be the likelihood function of a pdf, $p(n)=1-|n|$ for $|n|<1$?

This might seem like a basic question to some but I am utterly confused by the fact that the given pdfs are not Gaussian or any other distribution commonly seen in examples. I have two hypotheses ...
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20 views

Joint PDF of Complex Gaussian Vector

I want to find the joint PDF of vector $\mathbf{z}$ where $z_i=|y_i|^2, i=1 \dots N$ and $y_i$ is $i^{th}$ element of $\mathbf{y}=\begin{pmatrix} a_{1,1} & 0 & 0 & 0 &\cdots & ...
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25 views

Distance between two independent normal random variable

What is the PDF of $Z=\sqrt{(X-x_0)^2+(Y-y_0)^2}$ when X and y are i.i.d. zero mean normal random variable (i.e., $x\sim N(0,\sigma^2)$ and $x\sim N(0,\sigma^2)$)
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67 views

Badidas and Nikit Shoes

Good day everyone, I am self studying statistics at home and in the office whenever i have time. I want to improve my reporting. So i just came across this website and decided to try if could ask a ...
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3answers
68 views

Can I do a t-test to test significance? [closed]

I need a statistical test to determine if one group of ten classrooms with different numbers of students in each class has a class average on a test. Group two has 12 classrooms also with different ...
2
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1answer
53 views

Understanding $O_p$

One thing I feel like I have never mastered is the concept of $O_p$ convergence and how to use it. I understand the basic idea and what bounded in probability means, but I always have a hard time ...
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0answers
53 views

Show alias coefficient of Plackett Burman design equals $r_{ij}=\frac{c_{1i}'c_{2j}}{N}$

Consider a Plackett Burman design with N rows and let $\beta_{1}$ be the of the regression coefficients corresponding to the main effects and let $\beta_{2}$ be the vector of the regression coefficients ...
3
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1answer
28 views

Quantiles written as the expectation of a transformation?

Consider a continuous random variable $X$, with finite defined mean $E[X]=\mu$ and variance $E[X^2]=\sigma^2$. Notice that the variance of $X$ can be written as the expectation of a transformed ...
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15 views

Summary of Probabilities

I am trying to summarize the ages of a population of five people. I have the following observations with an "Average" calculated at the end: ...
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49 views

Ratio of CDFs $F(x)/x$ property

In my research project is useful to classify cumulative distributions functions of random variables with support in $[a,b]$ with $0\le a<b\le+\infty$ depending on whether the ratio, ...
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19 views

A way to check the accuracy of a Markov chain?

I posted the same question on MSE since I was not really sure whether to post it here first or not. Anyway since I still did not get any answers I will be posting this here hoping for some help. Say ...
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34 views

Probability distribution of time series

I am unable to understand concepts related to the probability distribution of binary time series. This is from the book Binary time series by Benjamin Kedem, vol 52 Let $X_t$, t =0,1,... be a binary ...
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0answers
19 views

prior predictive distribution negative binomial in R

I have a prior distribution Gamma(1.71,1.05) from a Poisson(2.2), and I know that the prior predictive distribution will be a Negative-Binomial of Gamma parameters i.e. Neg-bin(1.71,1.05). I would ...
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1answer
59 views

If $\frac{(2n-1)s^2}{\sigma^2} \overset{}{\sim} \chi^2_{2n-1}$, can I take the variance of both sides to get an equality relation?

I currently have a standard result regarding variances and it looks like: $\frac{(2n-1)s^2}{\sigma^2} \overset{}{\sim} \chi^2_{2n-1}$ that is, it is approximately a chi-squared distribution with ...