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

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2
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24 views

Which kind of mean (harmonic, geometric, arithmetic) is best suited for averaging probability ratios?

There are a bunch of examples around on how harmonic mean is more suitable for averaging rates, e.g. speed (when the distance is fixed). But what about probability ratios (p(A)/p(B), i.e. how much ...
0
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0answers
14 views

Nomenclature: What is the proper term to describe the probability of event A divided by the probability of event B?

I have a hidden markov model that scores the probability of various state sequences (paths). For simplicity, I will talk about a state sequence as an event. I am calculating how much more probable one ...
0
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0answers
17 views

Single Clerk Poisson Process Question [on hold]

Customers arrive at a ticket office window with a single clerk according to Poisson process with a rate of λ = 2 per minute. The office has a single clerk whose service times are i.i.d. exponential ...
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1answer
17 views

Jensen Shannon Divergence vs Kullback-Leibler Divergence?

I know that KL Divergence is not symmetric and it cannot be strictly considered as a metric. If so, why is it used when JS Divergence satisfies the required properties for a metric? Are there ...
2
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0answers
13 views

An example of r.v.s such that their distribution has more (conditional) independencies than their directed graphical model

I was trying to form an example where I had 3 r.v.s such that the distribution describing them had more conditional independencies or independencies than the directed graphical model corresponding to ...
1
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1answer
65 views

How can I determine if a poker application is “fairly” dealing hands? (Texas Hold Em)

I'm trying to take on a personal project with my new found knowledge (and beginner) in statistics and data analysis. I play an online poker app that is Texas Hold Em' (name withheld) and I suspect ...
0
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1answer
89 views

Probability Homework Question

A researcher is conducting a survey of county residents in a Midwestern state. Foolishly, she uses lists of registered voters as a sampling frame and randomly draws phone numbers and addresses from ...
2
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2answers
45 views

Probabilistic interpretation from sigmoid functions

Why do we interpret the results of logistic regression as probabilities? Passing the output of any regression procedure through a sigmoid function results in a probabilistic interpretation with ...
0
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1answer
247 views

Posterior Probability Question

a) Your initial belief is that a defendant in a court case is guilty with probability 0.5. A witness comes forward claiming he saw the defendant committed the crime. You know the witness is not ...
6
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0answers
34 views

Estimating number of balls by successively selecting a ball and marking it

Lets say I have N balls in a bag. On my first draw, I mark the ball and replace it in the bag. On my second draw, if I pick up a marked ball I return it to the bag. If, however I pick up a ...
4
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1answer
42 views

Given N samples from a population, can you determine or approximate the probability of the N+1 sample being within a certain range?

The question is as the title says: is it possible for me to determine the probability of the next sample ending up in a certain range? For example, lets say I pick N grains of sand from a bucket and ...
6
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4answers
137 views

Dungeons & Dragons Attack hit probability success percentage

In D&D players roll a 20 sided die trying to beat a set number to determine if an attack hits the target. Players often can add modifiers to this roll to help the odds in reaching this target ...
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1answer
27 views

Probability distribution, unfair coin

An unfair coin which has 0.35 probability to result head is tossed four times. Build and represent graphically the probability distribution and the cumulative ...
1
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2answers
47 views

Correlation of product of uncorrelated

This seems like it should be pretty simple but I'm not seeing it. Suppose I have two r.v.s X and Y with means of zero and variances of one, such that cov(X,Y)=0. What is cov(X,XY)?
1
vote
1answer
18 views

Is X a negative binomial? ( Tosses of dice)

Two dice are tossed independently until each pair has appeared at least once. Find the expected number of tosses needed and the standard deviation of this number of tosses. My attempt Let X be the ...
1
vote
2answers
137 views

How do I estimate P(X>Y) when given estimates for X and Y, for X,Y limited to the interval (0,1)? (Relevant to approximate sorting) [on hold]

How do I find a reasonable estimate for the probability P(X>Y) when given reasonable estimates of X and Y, where: I know that X and Y can take any values in the interval (0,1). The knowledge of the ...
2
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3answers
79 views

Rigorous real analysis book for probability theory

I have a Masters in math and I am currently doing a Masters in statistics. I am disappointed at the level of rigor in the proofs (and often outright omission of the proofs just a statement saying "in ...
2
votes
1answer
35 views

Difference between expectations of the same random variable wrt different probability measures

$X$ is a measurable mapping from a discrete sample space $\Omega$ to $\mathbb R$. $\mu_1$ and $\mu_2$ are two probability measures on $\Omega$. Assume they have probability mass functions $f_1$ and ...
0
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0answers
14 views

the probability of how many particles are active [closed]

I have a variable t that changes from 0 to 24. Then I two points a1,a2 and the distance between them is d. After that I generate m random variables between -b and b. These random variables ai are ...
4
votes
1answer
54 views

Glivenko-Cantelli Theorem

The Glivenko-Cantelli Theorem (http://en.wikipedia.org/wiki/Glivenko%E2%80%93Cantelli_theorem) states that if $F$ is a distribution function, $X_1,\dots,X_n \sim F$, and $\hat{F}_n$ is the empirical ...
3
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0answers
64 views

What does “independent observations” mean?

I'm trying to understand what the assumption of independent observations means. Some definitions are 1 "the occurrence of one event doesn't change the probability for another". 2 "sampling of one ...
0
votes
1answer
25 views

Mean squared error of a noisy random variable

Assume we have a distribution D, and a random variable X from this distribution. We want to estimate E(D) through X. Obv E(X) is an estimator for E(D). The question is that does the MSE (=mean squared ...
4
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0answers
94 views
+50

How to find the pdf from time series

This may seem trivial but I will appreciate help in determining the functional form of the probability density function (pdf) for the following case. Will highly appreciate some guidelines on how to ...
0
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0answers
18 views

Determine a distribution of a gaussian stochastic with different time

I would like to determine the autocorrelation function of a Gaussian stochastic. Let see my problem So my solution is The distribution of $y=x(t_1)-x(t_2)$ is also a Gaussian stochastic with ...
0
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1answer
31 views

Probability of a sum of values from a number of dice rolls

4 six-sided dice are rolled independently. Compute the normal approximation with continuity correction for the probability of rolling a total of at most 6. I have arrived at a point where I got that ...
0
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0answers
51 views

calculate probability for passengers who caught with gun [closed]

Can someone please give some clue? One strange phenomenon that sometimes occurs at U.S. airport security gates is that an otherwise law-abiding passenger is caught with a gun in his/her carry-on bag. ...
0
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0answers
58 views

what is true about s zscore [closed]

What the relation between score and mean, median? whihc is true from this ...
0
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0answers
14 views

getting posterior probability of the hypothesis of hypothesis

At any given time about 5.5% of women (age 15-45) are pregnant. A home pregnancy test is accurate 99% of the time if the woman taking the test is actually pregnant and 99.5% accurate if the woman is ...
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0answers
20 views

In Probabilistic Graphical Models, what does it mean that r.v. X influences r.v Y?

I wanted to pin down what the intuitive phrase: r.v. X influences r.v. Y as precisely and as rigorously as I could, and wanted to check if my interpretation was correct and complete with the ...
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1answer
36 views

Find out if I can ask for more

Scenario: I have a system that issues requests to another system. Each of these requests have a probability $p$ of requiring a specialized resource. The probability $p$ can be estimated using a ...
0
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0answers
8 views

Compare failure probabilities

I'm studying a process that may be used several times each year. For each time it is used I can calculate its failure probability and I also have a damage evolution law with the number of uses so I ...
0
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0answers
4 views

How many 3 digit even numbers can be formed using (0, 1, 2, 3, 4) and no repetition? [migrated]

My solution to the problem is as follows: The answer I get is 27. My reasoning is that the last digit must be even, so for that position there are 3 choose 1 possibilities. Then the first digit ...
6
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1answer
216 views

Numbers too large for R. How to approximate probability mass function?

Social network data is frequently found in a two-mode form: people vs. events they attend, people vs. classes they attend, countries vs. treaties they sign, etc. A strategy for analyzing this data is ...
6
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0answers
79 views

Bayesian modeling using multivariate normal with covariate

Suppose you have an explanatory variable ${\bf{X}} = \left(X(s_{1}),\ldots,X(s_{n})\right)$ where $s$ represents a given coordinate. You also have a response variable ${\bf{Y}} = ...
2
votes
2answers
37 views

Meaning of the expression $P(\theta_1,\theta_2,\theta_3) \propto 1$?

I am reading this statistics books and it keeps on repeating same expression over and over again $P(\theta_1,\theta_2,\theta_3) \propto 1$ What does the above expression mean?
0
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0answers
16 views

How to decide whether a given probability problem requires order or not

When solving a probability problem or calculating "n choose k", I am having difficulty deciding whether problem requires order or not. Are there any general rules of thumb that I can use while reading ...
0
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0answers
20 views

Bayesian Updating Process, 3 signals and 2 states of the world

Suppose Nature chooses a state $\omega = \{X,Y\}$ at $t=0$. Long-lived agents observe a signal $s_t$ at every period $t$, where $s_t = \{ x,y,z \}$. Agents all hold a common prior $\mu_0 \in (0,1)$ ...
3
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1answer
47 views

can we generate a random words from English letters that follow the bigram of the English language

The main issue is that several research building their solution of detecting and classifying English language is based on bigram distribution. However, I would like to know if it possible to generate ...
0
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1answer
25 views

Probablity calculation for at-least clause case

I saw the question: What is the probability of 1 out of 5 randomly selected people agree with the statement that men having more right for job compare to women? ...
1
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1answer
32 views

Can an a.s. (almost surely) finite random variable be a.s. UNbounded?

I thought that if a random variable, $\eta^2$, is assumed to be a.s. finite, then $\eta^2$ must be a.s. bounded. In the Martingale Central Limit Theorem in Hall & Heyde, they assume this: "let ...
2
votes
1answer
21 views

Chi-Squared Goodness of Fit Test Alternative? - Zero Can't Be in Denominator

I have 5 zones(categories) in which a certain percentage of total sinkholes exist. I have 5 different maps that I am testing to see which one provides me with the best fit to my expected percentages ...
1
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2answers
137 views

What probability distribution best describes my data?

I have a variable whose values are summated scale scores constrained within the range 3 to 21, inclusive. I considered this variable as a scale variable (though with restricted range). In order to ...
2
votes
1answer
105 views

maximum-likelihood of a sequence of events described by a Bernoulli distribution

I am having quite some troubles with the following homework: In a city it's measured for the whole year whether it rained or not. A distribution $\textrm{Bernoulli}(r_t|\rho)$ characterizes the ...
0
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1answer
24 views

Probability conditions [closed]

We have four coins (10 Cent, 10 Cent, 50 Cent, 50 Cent) and choose randomly two of them. The sum of the two coins is a random variable X. i) Show that the probability for X to be 20, 60, 100 is 1/6 , ...
14
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4answers
305 views

Bias in jury selection?

A friend is representing a client on appeal, after a criminal trial in which it appears that jury selection was racially biased. The jury pool consisted of 30 people, in 4 racial groups. The ...
1
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0answers
21 views

How to compare the distances or divergence between two groups of datasets

If I have two groups of data sets. Each group has two arrays of empirical data. In the first group each array has, say, 50,000 data points, and in the second group each array has 3,000 data points. ...
2
votes
1answer
51 views

Moment Generating Function of a nonlinear transformation of an exponential random variable

Let $\tau$ be an exponential random variable, with parameter $\lambda$. Let $$ V = \delta^\tau $$ where $0 < \delta <1$. Sorry if this notation seems strange, but it is what I am using, I ...
0
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1answer
35 views

How can I determine source type of a sequence?

I have sequences of binary events, e.g. $s=0001101$. I know that there are two types of sources $A,B$ possible generating each sequence. There are different conditional probabilities for a hit given a ...
0
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0answers
12 views

What's the Probability of having this Hypothetical Disease?

Question about disease transmission and infection: I want to know the odds of catching a disease and not knowing I have it, if the following conditions are possible: There is a 1/10,000 chance of ...
0
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0answers
17 views

Testing for consistency in survey data

I have a panel of 6 persons which each have generated 2 recipes (cooking), R1 and R2. I have then asked everyone in the panel to ...