Tagged Questions

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

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9 views

75% success, ranges for given sample sizes with 95% confidence

A given task has a 75% chance of success. With 90% confidence, what would be expected ranges of success for - 10 attempts - 50 attempts - 100 attempts - 1,000 attempts - 10,000 attempts very many ...
2
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2answers
40 views

Predictive with uniform likelihood

I'm trying to get a predictive density and currently getting something which I know can't be true (based on both logic and simulation based techniques. Here's the relevant information. $\theta$ is a ...
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0answers
18 views

Probability of seeing observation > x based on historical observations

I have a number of historical observations, let's say they represent the number of car accidents per day for a certain region. I don't know what the true distribution or probability is, but want to ...
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1answer
22 views

How to check if people think 3 is a lucky number while we throw with 2 dice

On the marketplace Gypsy accepts bets on two dice throw (he throws two dice at the same time, not one after another). Gamblers come and say what numbers will be on each of the two dice (it is a bet on ...
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0answers
7 views

Help required in finding the distribution of square root of distance in embedded space

The model generating the observation is of the form $y_n = A^Tx_n + U_n$ where $x$ is the output of a a linear stationary model and $U$ is a zero mean Gaussian noise of known variance. Now, $error ...
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0answers
41 views

Exponential random variable

The time it takes a printer to print a job is an exponential random variable with mean of 10 seconds. You send a job to the printer at 9:00 am, and it appears to be the fourth in line. What is the ...
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3answers
70 views

Probability that node A is connected to another node

Example: I have nodes A, B and C. A is connected to B and C. B is also connected to C. The link between two nodes have a probability to fail. For the link between A and B, the probability is pAB ...
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0answers
11 views

Use of Chi2 goodness of fit test with three-level nominal variables from two samples

I have two samples. One is comprised of people who did a pre-test but did not do a post-test (n=75). The other is comprised of people who did both the pre- and post-test (n=150). For each sample, I ...
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66 views

What Ratio of Independent Distributions gives a Normal Distribution?

The ratio of two independent normal distributions give a Cauchy distribution. The t-distribution is a normal distribution divided by an independent chi-squared distribution. The ratio of two ...
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1answer
25 views

How to bound a probability with Chernoff's inequality?

In my class, we were given Chernoff's inequality as $$P(X\le -t) \le e^{(-(\lambda*t - \log( E(e^{-\lambda*x}))))}$$ $$P(X\ge -t) \le e^{(-(\lambda*t - \log( E(e^{\lambda*x}))))}$$ It says that to ...
4
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1answer
72 views

Unintuitive interpretation of probabilities when doing logistic regression

The observations in my dataset can be split in two classes. The observations in class 1 are for sure correctly labeled. The observations that has been designated to class 2 have a huge percentage of ...
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1answer
26 views

Given a graph, identify users more likely to connect to a new user

I have some twitter-like data described as tuples of users (u1, u2), that means u1 follows u2. I also have a second dataset with another list of tuples (r1, r2), that means user r1 frequently click on ...
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0answers
10 views

reduce joint probability distribution of an image

I'm new in probabilistic graphical model. I'd like to know how the number of parameter needed to describe fully joint probability distribution of an image 10000by10000 that each pixel is 8byte (255). ...
4
votes
2answers
72 views

Expectation of $(X + Y)^2$ where $X$ and $Y$ are independent Poisson random variables

I would really appreciate anyone's help with this problem: (let $E$ denote expectation) Suppose $X$ and $Y$ are independent Poisson random variables, each with mean $1$. Find: $E[(X + ...
0
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0answers
25 views

Scoring function for categorical data

I would appreciate guidance on the following problem. There are three sets of urns, Set 1, 2, and 3. Each set contains the same number of urns, Urn 1, 2, 3. Each urn contains some number of Red ...
0
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0answers
64 views

Interpretation of priors in example

Suppose you have 3 variances $W_{1},W_{2},W_{3}$ that can be expressed as $W_{j}=q_{j}V$ with $j = 1,2,3$. According to one model, $W_{3}$ should be pronounced and $W_{1}$, $W_{2}$ should be small to ...
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1answer
26 views

How to find the joint distribution in embedded space

Euclidean Embedding of Co-occurr ence Data under Section 2, the problem formulation is given. In the paper link, the Authors find the distribution for lower embedding for the squared distances between ...
2
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2answers
50 views

The Mean of the number of times until an event occurs

Lets say we have 6 cards in a hat, that are all red. Now each time, we blindly take a card out of the hat: - If the card is red, we take it out of the hat and insert a blue card. - If the card is ...
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2answers
63 views

How to prove that the Fourier Transform of white noise is flat?

If we take $X_n$ a series a random vector with its components each having a probability distribution with zero mean and finite variance, and are statistically independent. How do we prove that the ...
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0answers
9 views

mean queue delay ( nonpreemtive priority)

I'm trying to solve a problem where all arriving items (arrival exponential $\lambda = 1/5$) are divided into into groups, those who are served within 5 units of time and those who have their service ...
3
votes
2answers
30 views

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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0answers
53 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?
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1answer
66 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 ...
0
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0answers
14 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 ...
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0answers
24 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
23 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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votes
1answer
71 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
61 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
votes
2answers
142 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
39 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 ...
1
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1answer
19 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
13 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 ...
0
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0answers
27 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
22 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 ...
0
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1answer
19 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
89 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
111 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
26 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 ...
0
votes
1answer
40 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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0answers
16 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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0answers
32 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. ...
0
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0answers
13 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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0answers
10 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 ...
4
votes
2answers
75 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
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. ...
0
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1answer
29 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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vote
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 ...
3
votes
2answers
34 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 # ...
0
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2answers
45 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. ...