# Tagged Questions

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

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### Poisson Approximation to Binomial

I have a Poisson approximation to binomial question, posted below. I'm not too sure if I'm using the proper formula: $$P(x) = e^{-np}(np)^x/x!$$ . Of anyone can tell me if I'm doing this ...
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### The distribution of STD/MAD for a Student [on hold]

Where X ~ a symmetric Student T Distribution $t_\alpha$, with power law tail $\alpha>2$, looking for the distribution of $\frac{(\sum_{i=1}^n x_i ^2 )^{½}}{\sum_{i=1}^n |x_i|}$, in order to ...
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### Testing hypothesis & $\alpha$

Hey I have a question that I found in a textbook for some practice before a test, but there aren't any solutions for it. I'm pretty sure it's related to testing a hypothesis, but I'm not sure. If ...
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### Member of multiple normally distributed populations

I'm writing a little tool for work and a stats question has arisen that is beyond me. In layman's terms: Let's say I've got a sample of 50 people who read the WSJ and their ages are normally ...
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I am given an exercise, and I can't quite figure it out. The Prisoner Paradox Three prisoners in solitary confinement, A, B and C, have been sentenced to death on the same day but, because ...
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### Adaptive Sampling to find maximum entities

Suppose I have N potential drugs, each of which have an unknown effect size(Flat prior). As I devote resources to clinical trials for each drug, the standard error of my estimate for the drug's effect ...
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### How do I calculate the probabilities in this decision making scenario?

I have the following problem: A decision has to be made. Paradoxically, there is value in only being marginally correct in making this decision, say I want to be correct 60 percent of the time. That ...
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### detector confidence

the situation is as follows: Say, I am going to answer a multiple choice question based on suggestion of my two friends. One gives correct answer 60% percent of the times, the other gives correct ...
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### Identify category for combination of words from categories of component words

I have the following matrix: ...
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### Distribution of sum of squares of T-distributed random variables

I am looking at the distribution of the sum of squares of T-distributed random variables, with tail exponent $\alpha$. Where X is the r.v., the Fourier transform for $X^2$, $\mathscr{F}(t)$ gives me a ...
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### What's the difference between a probability and a proportion?

Say I have eaten hamburgers every Tuesday for years. You could say that I eat hamburgers 14% of the time, or that the probability of me eating a hamburger in a given week is 14%. What are the main ...
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### I have a problem in bayesian networks get p(E|A)

I'm doing this book "Modeling and reasoning with Bayesian Networks" and I have this problem: ...
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### Probability statistics exercise, with not enough data?

I have a question connected with this exercise. In question a) I am supposed to calculate the probability using this formula $P(A \text{ and } B)=P(A) \times P(B|A)$. I think there is not enough data. ...
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### How can I prove that the cumulative distribution function is right continuous?

I've learned in my probability courses that the cumulative distribution function $F$ of a random variable $X$ is right continuous. Is it possible to prove that?
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### How would one use the pi-lambda theorem in determining that a CDF completely defines the distribution of a random variable?

The pi-lamda theorem states that if $Q$ is a pi-system contained in a lambda system $L$, then the sigma-algebra generated by $Q$ is also contained in $L$. We can use this to show that the CDF ...
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### Moralization and triangulation on belief networks

Assume that I have a belief network with a set of nodes. In order to create a valid junction tree I have to moralize the graph. Assume now that I have nodes with more than 2 parents (e.g 3 parents) ...
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### How to define a posterior probability of y given x when the model is not probabilistic?

Suppose we have a very simple online k-means where each new data-point is assigned to its nearest center (the mean is updated incrementally). Each center (cluster) is labelled with the most common ...
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### Calculating chance of event over time from sample data

I am doing the following experiment: I have slots which I monitor, the slot can either be occupied / free. The study is per slot, so we are discussing one slot here. Every now and then I receive the ...
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### Is the probability of a unique DNA match the same, irrespective of the size of the dataset?

One can argue that the evidential value of a database hit increases when the database gets larger. Indeed, having a unique hit in a database simply means that all the other persons in the database are ...
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### How to create a bivariate normal distribution

I have a data set like this: df Income Education_in_years 40,000 10 50,000 9 70,000 12 30,000 5 100,000 20 I would like to create a ...
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### Compute a probability using stochastic simulation

My problem is to solve the following optimisation problem using GA (Genetic Algorithm)and stochastic simulation. The goal is to solve the maximisation problem : \begin{equation*} \begin{aligned} ...
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### An unfair coin with different face value problem

Could any one give me some hints for the following problem: A coin has two face: 1 and -1/2, and the probability for 1 is $P(x=1)=1/3$ and for $-1/2$ is $P(x=-1/2)=2/3$. The expected value is ...
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### What characteristics of the distribution of a test statistic can be inferred using a bootstrap?

Setup: Let $p_n(x) = \mathbb{P}(S_n \leq x)$ and let $p_n^*(x) = \mathbb{P}^*(S_n^* - S_n \leq x)$, where $S_n$ is some zero-mean test statistic that can validly be bootstrapped, eg a sample mean, and ...
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### Unknown number of colours Bernoulli Urn

Okay, so, in the traditional Bernoulli Urn problem, we have an urn with a number N, possibly infinite, of coloured balls, and there are k possible colours. That one I grok. However, what if I don't ...
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### Bounds (or model) for estimating probability from generating process

I was curious if there was any bounds or approaches to getting good estimates for a probability from the following generating process. Suppose we have 2 sets of objects $A$ and $B$ where both sets ...
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### Substitution test for ANOVA?

I am working on biological dataset. Around 20000 genes of each sample are comparing with the same ones in another group in order to find significantly differentially expressed genes. I am comparing 3 ...
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### I have a question on conditional P with multiple events

I'm following this "Modeling and Reasoning with bayesian networks book's problems and Im stuck in this: ...
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### Determining conserved features using a Bayesian approach

I would like to perform some sort of binary classification, and my data set consists of 100 examples (for each class), which are vectors with 2500 elements. Ideally, I would like to determine which ...
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### Maximum likelihood estimation of volume

There is a metric called as the Volume V Can somebody explain to me how to find the value of V, which is the volume of a dynamical system. I need to apply maximum likelihood estimation on V to find ...
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### Compute the inverse of function [closed]

I want to compute and plot the inverse of given function f. I have the following code in R : ...
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### kde.test gives different p-values for similar KDEs

I have 4 sets of random floats between [0,1]: $d1, d2, d3, d4$. I need to compare these sets by pairs and I make use of the kde.test function of R's ...
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### Probability and Sampling distribution

Would you please explain me the difference between Probability distribution and Sampling distribution easily ? Is that the difference : in probability distribution we have probability for every ...
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### Number of trials needed to increment a counter variable

Truthfully I'm not even sure what the proper name for this sort of trial is, so I'll just describe the whole setup. Suppose I have an integer variable n, which starts at zero and gets incremented ...
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### Comparison of two curves

I have two measurements of something. You can think of them both as their own curve with known error on each point. They look quite similar, and if I calculate the R2 value it comes out to >0.9. But ...
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### Utility of Probability Generating Function [closed]

The utility of Probability Generating Function , how far known to me , is basically to generate PMF uniquely (what all the popular books of probability have written ) . Now , PGF is constructed with ...
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### How to visualise “equal in distribution” in the context of stochastic dominance?

I am reading about stochastic dominance in wikipedia. I don't comprehend the meaning of "equal in distribution". $x_B \overset {d}{=} (x_A+y)$ What does $\overset {d}{=}$ mean? I understand that ...
Suppose $X_1, \ldots, X_n$ are iid $\mathrm{Uniform}(0, 1)$ and let $X_{(n)} = \max(X_1, \ldots, X_n)$ and $X_{1} = \min(X_1, \ldots, X_n)$. How do I find the pdf of the sample range \$R = X_{(n)} - ...