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

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Probability selection of elements from a set

If we have a set $S= \{s_1,s_2,..,s_n\}$ and each element in the set $S$ has an assigned probability $P_n$. Then a selection process is applied to the set $S$ such that, each element $S_n \in$ $S$ is ...
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28 views

Probabilistic model Vs Weight based model

Can someone please explain what is the difference between probabilistic model vs weight based model with respect to ML context. When to use one over the other?
4
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2answers
50 views

Free Throw Probability

I was asked this in an interview today. Would you rather try to make 2/3 free throws or 4/6? Why? I reasoned that if my chance of making an individual shot was > 2/3, I would go for 4/6 because it ...
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0answers
13 views

Best way to graph probabilities of feature vectors

I have a lot of feature vectors in the form of: v1=[x0, x1, x2, x3, x4] where x0, x1, and x2 can take binary values. either 0 or 1 x3 and x4 can take values from 0 up to 9 I have a lot of vectors ...
2
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0answers
21 views

Expected numbers of distinct colors when drawing without replacement

Consider an urn containing $N$ balls of $P$ different colors, with $p_i$ being the proportion of balls of color $i$ among the $N$ balls ($\sum_i p_i = 1$). I draw $n \leq N$ balls from the urn without ...
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1answer
21 views

Joint PDF of a set of equations

I am looking for a way to find the joint pdf of vector $Z=[Z_1,Z_2,Z_3,Z_4]$ where $Z_1= a_1 X_1^2 + a_2X_1Y_1+ a_3 X_1Y_2 + a_4Y_1^2 + a_5Y_2^2$ $Z_2= b_1 X_1^2 + b_2X_1Y_1+ b_3 X_1Y_2 + b_4Y_1^2 + ...
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1answer
57 views

Probability that x samples from normal distribution sum to X

Lets assume that I have samples that fit to normal distribution. $f(x) = y$ How to calculate the probability that sum of values for $n$ next samples will equal $Z$. $\mathbb P(f(x1) +f (x2) + f(x3) ...
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1answer
51 views

Bootstrapping probability of success: what is wrong with my method?

I have a dataset where each row represents the outcome of individual bets placed by a population of players; each row has two fields: a player identifier and the outcome of the bet (1 if the player ...
5
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2answers
130 views

What is the probability distribution of $1-\text{mean}(|A-B|)$ where $A$ and $B$ are independent U(0,1)?

I'm not well versed in statistics so I'm not sure if my question is worded exactly correctly but basically here's the problem I'm trying to solve: imagine you have two equal sized arrays of size n. ...
0
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1answer
36 views

Range of predicted probabilities by logistic regression

I have a binary classification problem with unbalanced classes, e.g. I have 500 examples of negative class(0) and 20 examples of positive class (1) and I need to estimate the probability of positive ...
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1answer
12 views

Bayesian calculation of parameter multiplying normal

I am interested in a model like: $y_{i} = \sum_{k\in K}{\beta_{k} z_{k}}$, with $z_{k} \tilde{} N(\mu_{k}, \sigma_{k})$. where $\beta \equiv(\beta_{k})_{k\in K}$ is not known, but all else is. I ...
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0answers
12 views

Probability that the sample covariance matrix of a m.v. Gaussian exceeds a threshold

Let $\Sigma$ be a covariance matrix of $n$ data points in $\mathbb{R}^p$. So $\Sigma$ is $p\times p$. Suppose that the $n$ points are drawn from the distribution ...
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0answers
26 views

Pointwise probability limit

Suppose we have a joint distribution of a random sample $(y_n,x_n)\in R^2$: $$ y_n = \beta_0 x_n + \epsilon_n $$ and the estimator $$ \hat \beta = argmin_\beta \frac{1}{N} \sum_{n=1}^N(y_n - \beta ...
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0answers
21 views

Convergence of Monte Carlo sample average for arrays of random variables

Suppose $X_1$, $X_2$ are two independent real-valued random variables. Let $F$ be a continuous (unbounded) function from $\mathbb{R^2}$ to $\mathbb{R}$. Assume that the necessary measurability and ...
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13 views

markov proof for poisson process and question 2 [on hold]

I want answers for those 3 questions as soon as possible.I can't understad those stuffs.
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1answer
17 views

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
88 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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1answer
107 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
25 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
38 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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14 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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29 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
24 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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0answers
11 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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9 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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2answers
72 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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11 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
28 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
23 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
31 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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42 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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17 views

Normal distribution probabilities [closed]

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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1answer
51 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
52 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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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
121 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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0answers
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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0answers
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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0answers
33 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
46 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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0answers
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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74 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
64 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
63 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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26 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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70 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 ...