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

learn more… | top users | synonyms (3)

0
votes
0answers
16 views

How do I sample from a black-box model of a probability distribution?

I have a function 'P(x)' where we query for any 'x' it gives a probability value. This function 'P' does not have a closed form and the evaluation is costly. Now 'x' is a set of vectors(matrix whose ...
1
vote
0answers
14 views

Matches in 2 subsamples

So I have a sample of size N. I make 1 subsample from above sample with size n. (bootstrap sample) Then I make another one of the same size n. I wanted to compute the probability of having exactly k ...
1
vote
3answers
51 views

Second moment from survival function

Let X be a non-negative continuous random variable with probability density function f(x). Let $$G(t) = \int_{t}^{\infty} f(x)dx$$ Show that$$E(X^{2}) = 2\int_{0}^{\infty} tG(t)dt$$ My thoughts: I ...
0
votes
0answers
17 views

Time-partitions of sample size

I am struggling with explain something I read in a Whitepaper. The essence is as follows. Let's begin with a random variable $X$ defined as number of events in an hours. Further, we assume that $X ...
0
votes
0answers
18 views

Linear Probability Model Construction

I am dealing with a questionnaire consisting of 15 questions. I performed a factor analysis to all the questions and it has given three factors each consisting of 5, 7 and 3 numbers of questions ...
0
votes
0answers
126 views

Compute the probability that the provided classifier label is correct

A binary SVM classifier provides a label $y_c^{(i)}$ for each $i$-th sample provided. This is not assured to be corresponding to its true label $y^{(i)}$, since the classifier could have computed a ...
0
votes
0answers
12 views

Using the terms significance, probability or likelihood, in connection with estimators

Imagine a number of variates $x_i$, and a number of processes $P_k$ which depend on these variables, in an unknown way (ie no clear cut formulas to work with). Now consider the scenario where you ...
-2
votes
0answers
16 views

What is the area under the normal curve that describes the probability that more that 43 households have a gas stove [on hold]

HW 7.4 random variable will be approximated using the normal distribution
0
votes
0answers
18 views

What are the odds of having the same Lawyer make a mistake in two wills involving the same person? [on hold]

A lawyer made mistakes in my will and were caught while I was alive to have it fixed and then a loved one died and it turns out the very same lawyer made a mistake in his will that the deceased can't ...
0
votes
0answers
16 views

Why do we take the absolute value of weight of evidence when computing the information value?

I was looking at the explanation for Information Value calculation in STATISTICA and I find it a bit confusing: ...
0
votes
0answers
23 views

What are the odds of having 2 windows shot- one facing the west one year and another structure window the following? [on hold]

It is a small rural community with fields between our house and a hedgerow between us and the neighbors to the north, and different neighbors across the street with a field. It was always assumed ...
0
votes
1answer
33 views

What is obtained from the product of a probability and a log probability ratio?

I'm looking at the commonly used artificial neural network model that has nodes and connections. Quick refresher A connection has a source and target node, and a weight. The output of the source ...
5
votes
2answers
190 views

Stopping conditions in coin flipping sequence

Imagine you can flip a coin up to a maximum number of X times. You stop if during this sequence, the coin lands on tails 3 times in a row. Otherwise you keep flipping. You repeat this game some N ...
-1
votes
0answers
20 views

Is Experiment and Trial synonymous?

Here they define : When we repeat a random experiment several times, we call each one of them a trial. But here they give the subtitle Experiment or Trial. ...
0
votes
2answers
45 views

Are Event and Outcome synonymous?

Outcome : An outcome is a result of a random experiment. Event : A single result of an experiment. Are Event and Outcome synonymous ?
2
votes
2answers
28 views

Why is simulation used for probit choice probabilities?

As explained in this answer, the probability of a certain outcome in a Logit model can be written as $$ P=\int_{\varepsilon=-\beta'x}^{\infty} f(\varepsilon)d\varepsilon\\ = 1- F(-\beta'x) = ...
1
vote
0answers
14 views

How many random voting machines must be validated to be certain they are not biased? [on hold]

In Brazil often people question the results given by the electronic voting system. At the end of the elections, each voting machine prints a bill containing the votes it computed, and that same data ...
0
votes
1answer
25 views

Blackjack win probability, strategy

In blackjack, the probability of winning a hand played by the books is 48% (or so I've heard). Therefore the chance of winning three consecutively is 11% roughly. If I start from scratch 8 times and ...
2
votes
1answer
37 views

Square root of an inverse gamma distributed random variable

I work on the grouped t copula and try to replicate part of the following paper: "The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk ...
1
vote
1answer
28 views

Expectation with transformed random variable

The expected value of a function $f$ of a random variable $x\in R^n$ is defined as $E_x[f(x)]=\int p(x)f(x)dx$ where $p()$ is the pdf of $x$. Assume a function $h: R^m \rightarrow R$. Let $z=Mx$, ...
0
votes
0answers
12 views

Finding the underlying pdf by sampling “buckets” of values

The situation I'm looking at a system where I can perform the following trial: $N$ samples are randomly taken from a population of $V$ different values (which can be treated as categorical), ...
3
votes
1answer
52 views

Simple question on odds ratios interpretation

I am trying to interpret the Odds Ratios (ORs) from a multiple logistic regression model that compares the performance of various clinics in terms of preterm birth rate (measured as "Yes/No preterm ...
1
vote
2answers
77 views

asymptotic distribution of a statistic

Say we have iid sample of size $n$ with $X_i \sim Exp(\lambda)$ and the task is to find asymptotic distribution of the statistic $$T_n := \frac{\bar{X}}{s}$$, where $s^2$ is the unbiased sample ...
0
votes
0answers
18 views

Most-efficient/effective Incentive Scheme Design to Minimize Loan Default Probability [closed]

Here is an open-ended, hypothetical question regarding the optimization of a loan incentive scheme. Any and all suggestions/plans are welcome. Please ask any clarifying questions if you wish: A loan ...
2
votes
1answer
57 views

How to solve the ball drawing problem?

Suppose a basket contains $B$ blue balls and $R$ red balls. Then, suppose I pick $N$ balls from the basket. What is the probability that I get At least $b$ blue ones and $r$ red ones At least $b$ ...
0
votes
0answers
13 views

Probability distribution function with risk parameter

I'm looking for a way to adjust the probability distribution of a uniform random function I'm using in a program. I need to find a discrete probability distribution that accepts a "risk-aversion ...
2
votes
0answers
47 views

Combining two probabilistic predictions

I am solving a machine learning task in which I need to predict a label $\tau$ from input $\vec x$. The input $\vec x$ can be considered as two parts $\vec u$ and $\vec v$ ($\vec x$ can be thought of ...
0
votes
0answers
333 views

What does mean by PAC learning theory

I am new in machine learning field. I am studying a course of machine learning(standford university ) and I did not understand what's mean by this theory and what its utility. I am wondering if ...
1
vote
1answer
34 views

How do I calculate the probability that an event occurred by 1 of 2 independent processes when they occur together?

Suppose that I know the probability of an event occurring by either process 1 or process 2: process 1, p(event)=1-exp(-ax) process 2, p(event)=1-exp(-by) With this information, is it possible to ...
0
votes
0answers
22 views

Find the z-value for which the probability that a normal variable exceeds M + z(s) equals: [closed]

Find the z-value for which the probability that a normal variable exceeds M + z(s) equals: (a) .05000 (b) 0.3300 (c) 0.0980 (d) 0.3015
0
votes
0answers
12 views

how to compute the conditional expectation? [closed]

I am wondering how i could find the conditional expectation of U(X) given T=sum(Xi) The iid random variables are distributed as poisson. I know that U(x) is going to give a distribution of 1 ...
0
votes
0answers
23 views

how to calculate probability of a single member of a group having three characteristics/pre-conditions

In a study there are 72 members of a group A. How can I find the probability that any one member has all three of the following characteristics given what was known about the 72 members at the start ...
5
votes
2answers
120 views

$P[X=x]=0$ when $X$ is continuous variable

I know that for continuous variable $P[X=x]=0$. But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ?
0
votes
0answers
15 views

Theory of Runs on forex [closed]

I came across this theory of runs: Black-Red-Red-Red-Black which they give the probability of: 0.5**5 =0.03125 I would've picked 0.5**3 for the probability. Anyway, I thought I would test it on ...
-1
votes
0answers
10 views

survival analysis [closed]

Let’s say failure of a light bulb follows the exponential distribution with h(t) = 0.5, where t is in months. a) Calculate the probability that the light bulb will survive more than 3 months. b) ...
1
vote
2answers
63 views

Probability from normal distribution: < vs <=

I want to calculate the probabilities $P\{X < 0.5\}$ and $P\{X \leq 0.5\}$. $X$ is standard normally distributed. From what I have learned density function $\text{df}(x)$ I can get $P(X = x)$ ...
21
votes
8answers
1k views

The abundance of P values in absence of a hypothesis

I'm into epidemiology. I'm not a statician but I try to perform the analyses myself, although I often encounter difficulties. I did my first analysis some 2 years ago. P values were included ...
1
vote
1answer
43 views

Is the CDF really just a running total of the PMF or am I thinking about this wrong?

When using discrete variables (like the possible outcomes of rolling 2 die {1,2,3,4,5,6,7,8,9,10,11,12} ) is the CDF the same as a sum of the PMF? For instance, take my table below. This is the ...
5
votes
1answer
66 views

Prove $X_i$ in Span of $ X_k, k \neq i$

Let $(\Omega,\mathcal F, P)$ be a probability space and let $L_1$ be the collection of all integrable (finite expectation) real-valued random variables defined on this space. Assume that for $X_k\in ...
4
votes
1answer
657 views

When to use (and not use) the rule of three

The rule of three in statistics states that if an event is binomially distributed and does not occur with in n trials the maximum chance of it occurring is approximately 3/n. Suppose we have a ...
1
vote
1answer
40 views

How can I calculate this probability: $P(W_1<cW_2$) and $c\geq 0$?

Let $(W_t)_{t\geq 0}, $ be a Brownian motion. I want to calculate the following: $P(W_1<cW_2$) and $c\geq 0$ For $c=1$ it is easy. I just write it as an increment, but how can I do it when $c$ ...
0
votes
1answer
29 views

Random variables, inequalities involving them and medians thereof (II)

I have a continuous function $A$ for which it holds that: $$x\in S\implies A(x)<0$$ $$x\in T\implies A(x)>0$$ Of course, $S$ and $T$ don't intersect. Now consider two continuous ...
0
votes
0answers
10 views

How to calculate odds of excess occurrences

My question is on how to determine the percentage chance of an occurrence exceeding the expected number of occurrences. For example in poker, there is a 21.77% chance of an Ace appearing on the flop ...
1
vote
1answer
31 views

How to combine probability inequalities that are w.r.t. different random variables?

Let $x$ and $z$ be two independent random variables. Suppose I know the following two facts: $P_z[f(x,z) < g(x)] > 1-\delta$ uniformly for all x; $P_x[g(x) < h(x)] > 1-\delta_h$ How can ...
0
votes
1answer
48 views

Intuition for the Cauchy Quantile

I've got these two plots, the first is a plot of the cauchy quantile function evaluated at 500 random standard uniforms. The next plot is the cumulative sum of the qunatiles. For example, if elements ...
1
vote
1answer
25 views

likelihood of string of events given a string of probabilities

There are two classes of strings of events. E.g. A: 0,0,1,2,2,3,4,0,3,0,0,0 B: 0,0,0,0,3,3,2,1,5,6,7,0 Both class A and B strings exhibit variability. Many (e.g. ...
0
votes
1answer
33 views

Expected number of collisions for balls and bins problem

$n$ number of balls are thrown randomly to $m$ number of bins, standing in a row. The balls are labeled as $1,2,3,....n$ and bins are also labeled as $1,2,3,...,m$. The probability of $i_{th}$ ball ...
0
votes
1answer
18 views

Methods to weight probabilities that are being multiplied together?

I am trying to classify data according to a taxonomy: That is, given a feature vector $x$, I would like to compute: $P(A,\alpha)$ $P(A,\beta)$ $P(B,\delta)$ $P(B,\gamma)$ (You can think of the ...
0
votes
0answers
26 views

MECE statistics

Consider a sample of a real quantity $X$. Say that we divide this sample into two mutually exclusive and collectively exhaustive (MECE) groups. Say we know the mean and median of these two groups, ...
1
vote
1answer
55 views

Random variables, inequalities involving them and medians thereof

I have three facts which I know to be true and I am wondering if together they logically imply a fourth one (or not!). Consider $F_x$ and $G_y$ two continuous, uni-modal distributions on ...