A probability provides a quantitative description of the likely occurrence of a particular event.
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25 views
Identifying argmax result in information theory
I'm reading through a thesis at the moment which uses a "well known result from information theory", namely
$\mathrm{argmax}_\mathbf{g}\,\mathbf{f}\,\mathrm{log}\,\mathbf{g} = \mathbf{f}$,
for two ...
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0answers
20 views
Logit: what does irrelevance of the benchmark mean?
In McFadden - Analysis of Qualitative Choice Behavior, Axiom 3 (Irrelevance of Alternative Set Effect) states:
The function $V(s,x,z)$ determining the selection probabilities in
$P(x|s,B) =\ ...
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votes
1answer
36 views
Probability distributions
What is the probability that a random number [0,1) will lie in [0.5,0.6]?
As far as I know, there are 3 probability distributions in physics we usually use, but I am not sure when we can use ...
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0answers
29 views
How to calculate probability with sigmoid output in feedforward neural network?
first of all I'm sorry for my not very skilled English, but I will do my best to explain my problem.
I'm trying to create a feedforward neural network with one hidden layer (with probably arctan ...
3
votes
1answer
61 views
Probability over $50$-day ranges to predict results on one day
The title is a bit complex, so I'll just post the question. This is in preparation for a final I'm going to take.
Consider the total number of cars that a car dealership might sell over $50$ ...
8
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0answers
96 views
Product of two independent random variables
I have a sample of about 1000 values. These data are obtained from the product of two independent random variables $\xi \ast \psi $. The first random variable has a uniform distribution $\xi \sim ...
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2answers
65 views
Finding the probability of given model
I'm trying to model a system given as a project, any help or advice is useful for now.
Here our assumptions for a part of it:
If I study for the finals and do assignments, I have $80\%$ chance to ...
1
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1answer
46 views
Finding conditions on unspecified CDF that permit a solution to an equation
[A duplicate thread can also be found at http://mathoverflow.net/questions/131142/finding-conditions-on-unspecified-cdf-that-permit-a-solution-to-an-equation ]
Let $F(\alpha) := ...
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13 views
Importance sampling of finite path of stochastic difference equation
Before passing to question, let me briefly recap what's importance sampling of random variables is about. Suppose $\xi$ is a real-valued random variable with density $f$, and let $g:\Bbb R\to \Bbb R$ ...
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0answers
19 views
Random variables resulting due to single or multiple experiments
Assume there are ‘n’ entities that collect some data after each ‘t’ time instances. Generally their collected data is within an “expected” range. However, occasionally the data exceeds the “expected” ...
1
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1answer
37 views
Expected peak to trough calculation
I am having trouble coding up in R equation 3.1 in the following paper: http://www.intelligenthedgefundinvesting.com/pubs/rb-cb.pdf
My function:
...
2
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0answers
43 views
A question regarding the central limit theorem
I would appreciate if you could please take a look at the following attempt. I am preparing for an upcoming exam, and this is taken from a past exam paper. I would like to know if it is correct. Thank ...
4
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0answers
36 views
Estimating repeat shoppers from an incomplete sampling
I'm trying to estimate how many people visited the farmers market once, twice, thrice, etc. in a given time period, using sampled data. We have interview data from approximately 50% of visitors as ...
1
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0answers
38 views
Question about proof for luce choice axiom w.r.t. conditional probability
In Luce (1959) the choice axiom is definied, that for a finite subset $T$ of $U$ such that, for every $S\subset T, P_S$ is defined.
If $P(x,y)\ne 0,1$ for all $x,y\in T$, then for $R\subset S\subset ...
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votes
1answer
33 views
Working out probability with alpha and beta
Working out probability with alpha and beta?
Let's say in an experiment, the Null hypothesis is patients having Condition A. Alpha (type I error) is 0.05 and beta (type II error) is 0.15.
If i have ...
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0answers
21 views
Partials of PDF with no closed form solution
I need to estimate partial derivatives for all N parameters denoted $\theta_{N}$ of a probability density function(PDF) $\mathcal{f}$.
This PDF $\mathcal{f}$ has no closed form solution and is ...
5
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0answers
117 views
Luce Choice Axiom, question about conditional probability
I'm reading Luce (1959). Then I found this statement:
When a person chooses among alternatives, very often their responses
appear to be governed by probabilities that are conditioned on the
...
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0answers
24 views
How to calculate probability contingent on multiple events?
This isn't a homework problem, but something I just thought of when watching a crime show.
If I am trying to determine the probability of [insert Conclusion] or C, and I know C is comprised of A ...
2
votes
1answer
33 views
Detect bias in subset of Bernoulli processes
I'm looking for advice on the best method to use to answer this question.
General scenario:
We have multiple testing machines A,B,C,D etc. each tests a identical randomly selected part and provides ...
4
votes
3answers
118 views
Problem with p-values from A/B testing
I'm pretty confused right now and the more I look at it, the more confused I get. Overthinking!
I'm doing some A/B tests for my website. I'm using the significance calculator that's in this article:
...
1
vote
2answers
92 views
Function with variable having gaussian distribution
If I have a variable $X$ whose Gaussian distribution is known and let $f$ be a known function, is there a way to compute $f(X)$ i.e. the resulting Gaussian distribution from this? Is the result ...
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0answers
51 views
Distribution of independent binomial variables conditional upon the sum
Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim Binomial(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is distributed ...
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0answers
51 views
satellite radios has a 3% defective rate. A random sample of 1000 radios is drawn. What is probability the defective rate is greater than 5%?
The assembly line that produces satellite radios has historically resulted in a 3% defective rate. A random sample of 1000 radios is drawn. What is the probability that the defective rate is ...
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0answers
29 views
Hilbert curves: bounds / probabilities of preserving neighbors
Hilbert Curves (Wikipedia) are space-filling curves said to "fairly well preserve locality".
Do you know any theoretical results here, such as bounds that neighbors within a radius of $\varepsilon$ ...
1
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1answer
38 views
Probability of $C_n^k$ elements which contains at least K elements
I'm trying to do a simple problem.
I have a set of integers:
$$N={1, 2, 3, 4, 5, 6} $$
I want to combine this elements in a set of combinations of size $k=3$ from this set, i.e. $C_6^3$, where ...
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0answers
14 views
Randomization testing in Bayesian spatial scan statistics
I was reading about Bayesian Spatial Scan statistics paper. I have this confusion about why randomization testing is not necessary in this approach. The paper says that it is by construction. But, I ...
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0answers
27 views
Optimizing a Poisson Process
So, I was standing in line for a Paramore concert for a very long time this past weekend because the boyfriend wanted to be up front during the show. I got to thinking, what would be the optimal time ...
1
vote
0answers
49 views
Mean and variance of call center data
I have a fairly involved homework question, I was wondering if I could get some help.
There are two types of phone calls arriving at a switch, long-duration and short-duration. Each day the number ...
2
votes
1answer
88 views
Asymptotic probability concerning the largest absolute value in an iid Gaussian sample
Let $v[n]$ be a vector $N$ $iid$ gaussian samples, of ~$N(0,\sigma^2)$ Also, let $v_{max}$ denote the maximum absolute value of all the samples given. (That is, if I took the absolute value of all the ...
1
vote
1answer
56 views
How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
2
votes
1answer
175 views
Should I expect it to be a chicken or a penguin?
An alien is trying to classify a group of only chickens and penguins into, well, chickens and penguins by analyzing 3 independent boolean features A, B, C.
If the animal (in reality) is a chicken, A ...
1
vote
2answers
36 views
How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
1
vote
1answer
56 views
Z test of coefficients of output?
I have fitted a certain ARMA model and got the following output:
As you can see, some coeff were set to zero and the focus is on the ma5 coeff and the intercept. To be exactly, the ma5 coeff is ...
3
votes
1answer
63 views
Neg Binomial and the Jeffreys' Prior
I'm trying to obtain the Jeffreys' prior for a negative binomial distribution. I can't see where I go wrong, so if someone could help point that out that would be appreciated.
Okay, so the situation ...
0
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0answers
59 views
How to compute $f(R_1,R_2)$ from $f(R_1|X_1)$ and $f(R_2|X_2)$ given $X_1, X_2$ are dependent RVs?
Given
$R_1=g(X_1,Y_1,Z_1)$ and $R_2=g(X_2,Y_2,Z_2)$
$Y_1,Y_2$ are iid jointly Normal
$Z_1,Z_2$ are iid jointly Normal
I have computed the conditional pdfs $f(R_1|X_1)$ and $f(R_2|X_2)$ and know ...
2
votes
1answer
20 views
send a packet with probability p
I have a computer network and I want to choose random connections between them. How can I randomly choose different connections between the nodes? For example, a node sends a packet and chooses the ...
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0answers
21 views
spss 20 for mac: how to get probabilities after running a binary logistic regression [duplicate]
I have a binary variable that I'm investigating in SPSS, inclination_to_dance. I have another linear variable as well, ...
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0answers
25 views
Probability that a given Normal Distribution is Maximum among others [duplicate]
You are given the mean and standard deviations of N normal distributions x1,x2...xn
What is the probability that x1 is maximum?
ie. Find P(x1>x2,x3..xn)
How do I go about solving this?
x1,x2,x3 etc ...
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votes
1answer
62 views
Probability to be less the expectation
Let $D$ be a positive random variable with $\mathrm{E}[D] < \infty$. Assume that there exist $y>0$ and $\epsilon>0$ such that: $P(D > \mathrm{E}[D]+y) > \epsilon$. Prove that there ...
0
votes
1answer
31 views
Calculating probability in questionnaire answers
I'm designing a piece of research and want to quote the probability of two unique responses matching.
10 questions, for each answerer is required to select a,b or c. Therefore, if selecting randomly ...
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0answers
13 views
If I randomly execute tasks working on some subset what can I say about total coverage of the set over some time period?
Say, there are 5 task to be executed with the following probabilities:
Task-A: 0.6
Task-B: 0.2
Task-C: 0.12
Task-D: 0.05
Task-E: 0.03
Each task works on some subset $k_i; i = 1..5$ (for each task ...
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2answers
30 views
Transform hazard rates to other time intervals
If a population has a hazard rate of $X$ per year, what would be its hazard rate per month or per day?
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0answers
31 views
Probability: A Card is drawn from a standard deck of 52 playing cards [closed]
A card is drawn from a deck of cards what is the probability of drawing a spade not a face card?
3
votes
1answer
39 views
Expected number of duplicates (triplicates etc) when drawing with replacement
I have the following problem:
I have 100 unique items (n), and I'm selecting 43 (m) of them one at a time (with replacement).
I need to solve for the expected number of uniques (only selected once, ...
1
vote
1answer
56 views
Moment generating functions question
Suppose that $X_1, X_2, ..., X_n$ are independent, where each $X_i$ has probability (mass) function $p_i(x_i)$ given as $p_i(x_i) = \frac{e^{-\lambda} \lambda_i^{x_i}}{x_i!}$ (only the parameter ...
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1answer
43 views
Conservative confidence interval
One month before the election, a poll of a large number of randomly selected voters showed 65% planning to vote for a certain candidate. The newspaper article reported a 90% conservative margin of ...
4
votes
3answers
193 views
Probability the sum of numbered balls drawn from a box is odd
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box, what is the probability that the sum of the 3 numbers on the balls selected from ...
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1answer
39 views
How can I predict a value like this from a bayesian network model?
Let $\theta$ be the set of parameters for a Bayesian Network model. The model observes some data $D$. I want to then predict the values of some new data $D$. Why is the following true?
$$
p(D'|D) = ...
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0answers
28 views
Predicting Risk based on weighted data
I am looking for a formula I can use in Excel that will provide a risk score from 1 - 10 with 10 being high risk. I have a set of 15 data items (i will add more in future) which are weighted on a ...
5
votes
2answers
79 views
Distribution for number of trials before a fixed sum is reached
I'm trying to figure out the distribution over a number of trials until a stopping condition is met. In particular, imagine we are observing samples of a uniformly distributed random variable, $X \in ...
