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

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Finding average number of rolls for recursive rolls on success

If there is more appropriate terminology to better phrase my question, please edit. Imagine I have a 3 sided die: two faces marked 0, one face marked 2 Whenever a two is rolled, two more rolls are ...
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1answer
38 views

Distribution of a logit transform of a normal variable

If I have a normal distribution with a given mean and variance and apply a logistic transform to it, what is the mean and variance of my transformed variable? This seems like it has to be a well ...
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17 views

K-Nearest-Neighbors Probability Distributions

I have a question about K-nearest-neighbors and whether it is possible to output more estimates than just the weighted estimate that the R package KKNN package gives you. I am predicting sports ...
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3answers
38 views

Probability of a certain run of dice rolls

OK, so here's a simple problem: Suppose I roll a D6 one hundred times. What is the probability of any number appearing exactly 50 times? Now, the probability of rolling 50 ones is presumably given by ...
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31 views

Average Power Density Based On Weibull Probability Density Function [closed]

I want to generate a graph of the power density against the mean wind speed at each station for a period of 5 years.. on one graph i want, for 5 years for 1 station.. and also the weibull curve for ...
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38 views

Combining evidence using Dempster-Shafer theory

Can someone post a simple explanation of Dempster-Shafer theory? There are lot of links available but the reading material in those sites is academic in nature and time consuming to read and ...
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2answers
58 views

Regression and point-specific p-values (using R for explanation)

Consider the following (in R): library(MASS) plot(stack.loss~Air.Flow,data=stackloss) regression <- rlm(stack.loss~Air.Flow,data=stackloss) abline(regression) ...
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1answer
29 views

Finding a probability mass function for $[x]$ is defined as the largest integer $n$ such that $n \leq x$

If $X$ is an exponential random variable with parameter $\lambda$ and we have that $[x]$ is defined as the largest integer $n$ such that $n \leq x$. If $Y$ is defined as $$Y = \left[ X\over a ...
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44 views

Likelihood Function [closed]

$n$ random variables or a random sample of size $n$ $\quad X_1,X_2,...,X_n$ assume a particular value $\quad x_1,x_2,...,x_n$ . $\bullet$ What does it mean? The set $\quad x_1,x_2,...,x_n$ ...
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2answers
59 views

Probability of period without event

I have a data set of a list of invoices each of which have a date. I'm trying to detect when I might consider that a customer has stopped ordering a part. The way I'm approaching this might be ...
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1answer
51 views

Estimating the probability of next failure?

I have some data about how some components failed. They can either be replaced in whole or have some of their sub-components repaired. I would like to know if there is a way to fit a failure model to ...
2
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1answer
50 views

Statistics wording question

I am reading a statistical procedure trying to figure out and understand what's going on. The statement says "Compute the posterior on $\mu$." Does this mean compute $p(\mu)$? Does this mean ...
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1answer
43 views

Modelling uncertainty with probability distributions

Suppose we’re building a system with certain qualities that we’re interested in, e.g. response time, battery usage, etc. Each of the system’s qualities depends on our decision about components we use ...
2
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0answers
33 views

How to calculate the log likelihood in HMM from the output of the forward algorithm in R?

How can I get the log likelihood or the probability value from the forward algorithm for an observed sequence? For example, when I executed the forward algorithm in ...
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0answers
49 views

6-sided die roll average value [duplicate]

A die is rolled 100 times. Find the probability that the mean value would be between 3 and 3.5. I've found the expected value which is 3.5 without idea what to do next.
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32 views

Explain probability measure and probability distribution

Dear statistics community, I seek your help to understand the jungle of concepts about probability theory. I am struggling to form a coherent understanding of terms like probability mass function, ...
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1answer
100 views

Probability that a random number will be the largest from sets

Let's say that I have three ranges of numbers: $$ A: [0.15, 0.26]\\ B: [0.25, 0.34]\\ C: [0.20, 0.35]$$ If a number was randomly picked from the range of each set, what is the probability ...
2
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1answer
82 views

Why is the probability zero for any given value of a normal distribution?

I noticed that in the Normal distribution, the probability $P(x=c)$ equals zero, while for the Poisson distribution, it will not equal zero when $c$ is a non-negative integer. My question is: Does ...
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43 views

Why we use infimum in the definition of Quantile function

I looked up the definition of Quantile function in Wikipedia, it is said that: The Quantile function is $Q(p)=\inf\{x\in R:p\le F(x)\}$ for $F:R\to(0,1)$, for a probability $0<p<1$, the ...
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1answer
54 views

Understanding the two-stage choice paradigm

In Manski - The structure of random utility models the following example is proposed: Consider the alternative set space a = $(\alpha,\beta,\gamma)$ with the attribute representation: $X = ...
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2answers
83 views

Intuition for cumulative hazard function (survival analysis)

I'm trying to get intuition for each of the main functions in actuarial science (specifically for the Cox Proportional Hazards Model). Here's what I have so far: $f(x)$: starting at the start time, ...
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0answers
42 views

A question on the exponential distribution [closed]

I am wondering if you could help me with the following: Charlie and Bella and their friends Mark and Leonard each have a toy. Each toy breaks at a time that is exponentially distributed with ...
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44 views

Possible outcomes in a soccer match [closed]

If ten (10) matches are played, I want to find out how I can calculate the probability of the outcome being: Between 3 and 7 home wins Between 1 and 6 draws Between 1 and 6 away wins (The ...
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0answers
21 views

Does a random variable of t-square converge almost surely to another random variable?

Does a random variable of t-square converge almost surely to another random variable? Here is the random variable $Tn$: $$ Tn=\frac{Z_{0}}{\sqrt{\frac{1}{n}\left ( ...
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2answers
94 views

How can I calculate the relative probability of each move resulting in a win, given historic win/loss data for the possible moves?

We are at a position in a game where there is a decision to be made. As there are relatively few game positions and possible moves, we have collected statistics from previous occasions the game was ...
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2answers
104 views

Trying to understand formula for the Survival Function (survival analysis)

I'm trying to learn the Cox Proportional Hazards Model on my own, and found this link that describes it in clear terms. But when I get to Formula (5) ($S(t) = \exp(−H(t))$) I can't figure out where ...
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1answer
78 views

Probability of a subsequence occurring simultaneously in two longer sequences

Suppose I have two sequences of characters of length L and M respectively, with the characters chosen i.i.d. from an alphabet of A through H, each with probability p=1/8. I want to find the ...
3
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1answer
48 views

Probability of reaching a threshold after several trials

I was wondering if there wasn't some better way to get to the bottom of this question I had regarding the chances of reaching a certain threshold of guessing numbers correctly over a series of trials. ...
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0answers
47 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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42 views

What is the meaning of McFaddens Axiom: Irrelevance of Alternative Set Effect?

On page 110 of McFadden,1973 - Conditional logit analysis of Qualitative Choice Behavior, Frontiers in Economics, ed Zarembka, New York: Academic Press, pp. 105-142 the following three Axioms are ...
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1answer
39 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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66 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 ...
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1answer
66 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 $50$ ...
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159 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
80 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 ...
2
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1answer
53 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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1answer
54 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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21 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” ...
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1answer
44 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: ...
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52 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 ...
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40 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 ...
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45 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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1answer
38 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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22 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 ...
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143 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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26 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 ...
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1answer
37 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 ...
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3answers
148 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: ...
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2answers
99 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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56 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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