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

learn more… | top users | synonyms (3)

1
vote
1answer
39 views

Negative Binomial Distribution R

This question was given in class and I was wondering how to do this in R: "Sixty percent of a large lot of old spark plugs are still usable, and they can be individually tested to determine this. Let ...
1
vote
1answer
29 views

Regression function of “non-regressible” data

I have some background in probability, and now trying to understand statistics, which sometimes leads to the questions of the following kind. Let $X$ and $Y$ be two random variables that represent the ...
2
votes
0answers
26 views

Does Hoeffding's inequality apply to sampling from finite populations?

Based on Hoeffding's theorem, one could easily find the minimum number of samples required for the inequality $\Pr \left(|\bar{X} - \mathrm{E} [\bar{X}]| \geq t \right) \leq \delta$ to hold as ...
0
votes
0answers
20 views

Calculate probability of consecutive event from R simulations

he problem is to calculate the PMF of consecutive flips of head (M) in N number of coin flips. Consecutive heads, k=0, 1, 2,...,N, the PMF is P(M=k). I use $sample(0:1,N,rep=T,prob=(0.25,0.75))$ to ...
1
vote
1answer
27 views

Calculate probability of consecutive event from R simulations

The problem is to calculate the PMF of consecutive flips of head (M) in N number of coin flips. Consecutive heads, k=0, 1, 2,...,N, the PMF is P(M=k). I use ...
1
vote
0answers
13 views

How to calculate confidence limits for various scenarios when drawing random cards from a pack?

I'm designing an experiment that involves a subject attempting to determine various attributes of a playing card drawn at random from a standard 52 card pack. The experiment is in four phases: ...
0
votes
1answer
9 views

Picking 3 coins from 6 coins without replacement. What is probability of getting a nickel on a certain pick?

I'm having trouble with this problem: There is 1 nickel, 2 dimes, and 3 quarters in a cup. You pick 3, one at a time, without replacement. What is the probability of getting a nickel on the first ...
11
votes
3answers
218 views

Uniform random variable as sum of two random variables

Taken from Grimmet and Stirzaker: Show that it cannot be the case that $U=X+Y$ where $U$ is uniformly distributed on [0,1] and $X$ and $Y$ are independent and identically distributed. You should not ...
0
votes
0answers
22 views

Sampling from a multivariate distribution

Given $X = [X_1 X_2 \ldots X_n]^{\top}$ is a vector of independent bernoulli random variables and $A \in \{0, 1\}^{m \times n}$ is an arbitrary boolean matrix. Define a random variable $Y$ as $$Y = ...
1
vote
1answer
33 views

Need direction in regards to probability based random value generation

I have a daily stream discharge data set spanning 10 years whose histogram looks like this: I would like to use it to set the distribution for a randomly chosen discharge for a given timestep. That ...
2
votes
1answer
183 views

Area within a given number of standard deviations from given mean

I have a variable with mean value of 18.85 and standard deviation of 1.45. I want to define the area that is covered by 1.45 standard deviations left and 1.45 standard deviations on the right side ...
1
vote
0answers
30 views

How to estimate the correlated individual components from a sum, for a random process?

Assume that there are $N$ realisations of five individual, random variables$X_1$, $X_2$, $X_3$, $X_4$ and $X_5$, which in general could be correlated. We define another random variable ...
0
votes
0answers
28 views

Formula the conditional probability of marbles [on hold]

I have a interesting question that need your help. I have two sets A and B. Set A have 10 marbles that numbered from 1 to 10. Set B have 6 marbles that numbered from 1 to 6. Randomly choose $g$ ...
5
votes
1answer
116 views

How to calculate $P (|X − Y | ≤ 1/6)$? [duplicate]

$f_{X,Y} \left( x, y \right) = 1\quad \text{for}\quad 0≤x≤1,\ 0≤y≤1 $ and $0$ otherwise. How to calculate $P \left( |X − Y | ≤ 1/6 \right)$?
4
votes
2answers
55 views

Gibbs Sampling and Probability Notation

Problem 1 I am trying to implement Gibbs Sampling for the following problem: There is a grid measuring 3 x 3 sites, each "site" can be designated in a state, $X$, of 1 or -1. The sites are numbered ...
5
votes
1answer
123 views

Probability of getting the correct direction, given you get the same answer

A town is composed of $2/5$ out of town couples and $3/5$ in town couples. If a couple is from out of town, the probability that the husband and wife will give you the correct directions ...
1
vote
0answers
38 views

Rate of convergence of the coverage probability of bootstrap confidence intervals

I was wondering if someone knows good books or references that deal with this subject : "The rate of convergence of the coverage probability of bootstrap confidence intervals" Many thanks for your ...
-1
votes
0answers
21 views

My naive bayes classifier doesn't show probabilities [duplicate]

I'm trying to predict the probability between 1-0 and have found that naive bayes is supposed to show this, however when I use it I only have ...
2
votes
1answer
72 views

How to estimate the individual components from a sum for a random process?

We have $N$ realisations of five individual, IID random variables $X_1$, $X_2$, $X_3$, $X_4$ and $X_5$. We define another random variable $S = X_1+X_2+X_3+X_4+X_5$. Now, for a given $S$ generated from ...
0
votes
0answers
28 views

Trying to find a classifier that will give me probability predictions between 0-1 in weka

This is the first time I've done any sort of predictive modelling and I think I've really confused myself. I have a training set of data with a column at the end that has either a 1 or a 0 in it. ...
2
votes
1answer
41 views

What sampling method will be suitable when there is no published list is available?

As there is no published list of population (employees), how can I select my sample? Even if I want I can not go for judgmental sampling as the academicians in my University strongly disagree for ...
6
votes
1answer
81 views

What are some good references on how probability theory got mathematically rigorous?

I am working on a term paper for an analysis course and I thought it would be interesting to talk about the connection between analysis and probability theory. Honestly, it would also benefit me a lot ...
2
votes
1answer
24 views

Combination/permutations question where repetition is allowed

So I guess this is a combination/permutations question where repetition is allowed. What is the % chance that six six-sided dice will show at least 3 duplicates of the same number or that there will ...
0
votes
0answers
15 views

Conditional and joint pmf of sequences of random variables

I have random variables $X_1...X_N$ which are Poisson($\theta$) distributed. I also have inclusion indicators $Y_1...Y_N$ which are Bernoulli($\pi$) distributed. These indicate whether $X_i$ is ...
1
vote
1answer
57 views

What is the probability that a girl is taller than a boy, with boys ~N(68, 4.5) and girls ~N(62, 3.2)?

"Given that boys' heights are distributed normally $\mathcal{N}(68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal{N}(62$ inches, $3.2$ inches$)$, what is the probability that a girl ...
0
votes
1answer
19 views

joint probability distribution with a constant

If $X \sim N(0,1)$, then what is the joint probability distribution of $(X+1,X)$? An attempt: $f(x,x+1)=f(x|x+1)f(x+1)=f(x+1)$, so $N((0,0),(0,0;0,1))$. Note sure though...
0
votes
0answers
2 views

Softmax factorization for a hidden markov model

I'm trying to formulate a hidden markov model where the transition and emission probabilities are governed by a softmax distribution. I'm not sure if this is a good idea, but I thought it could be ...
4
votes
1answer
38 views

Conflicting formulae to determine the probability that an event has occurred

Assume a molecule that at each time step has a probability $p$ of being removed from the body. After one time step, it seems to me that these probabilities exist: Molecule still in body: $1 - p$ ...
2
votes
0answers
20 views

Can the law of total covariance apply to variables from different sample spaces?

Wikipedia says this about the law of total covariance (http://en.wikipedia.org/wiki/Law_of_total_covariance): In probability theory, the law of total covariance,[1] covariance decomposition ...
0
votes
0answers
23 views

how to test for significant preference with two variables with different number of outcomes?

In a random choice trial with two parameters (color and location), I want to test whether a choice is influenced / driven by one other factor or the other, or whether they are independent. In detail: ...
2
votes
1answer
93 views

Convergence of $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$ if $X_1, \dotsc , X_n \sim U(0,1)$

$X_1,X_2,\dotsc ,X_n$ are independent, uniformly distributed random variables on the interval $[0,1]$ The question is the convergence of the sequence: $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$. ...
2
votes
1answer
42 views

What's the statistical method where you add a certain number to each sample to make the distribution slightly more uniform?

Please forgive my lack of knowledge - it's been a while since I've taken classes in statistics, and even then, it was not my strong point. I'm trying to recall a method used to upweight all values in ...
0
votes
0answers
15 views

How to estimate Extreme value distribution parameter

Assume that I have non-negative Gamma random variables $\{X_i,i=1\dots n\}$ and I want to find $M_n=\max\{ X_i\}$. I want to apply generalized extreme value distribution (GEV), but how to find $\mu$, ...
0
votes
0answers
6 views

comparing probability of imbalance classes

I am trying to figure out what id the standard way to compare the probability of occurrence of two imbalances classes: let say there 1500 web pages with different languages edition (e.g. Wikipedia). ...
0
votes
0answers
13 views

Iteratively re-weighted least squares

I am a frequent user of Emblem and I am trying to develop my understanding of the modelling process by understanding how exactly Emblem fits the models. To achieve this I have taken a very simple ...
1
vote
0answers
22 views

Calculating the probability of both teams to score in a soccer match?

New to the forum, and while not quite an idiot, I have no where near the knowledge and nous of all in here. Consider the following scenario: Soccer match Home team - Team A Away team - Team B ...
0
votes
0answers
17 views

How normalize this distribution probabilities [closed]

I have these probability distributions, how can I normalize then calculating the Kullback Leibler divergence ? ...
2
votes
1answer
38 views

Does the “joint probability” of two events take their order into account?

When we speak of "joint probabilities" in a general sense, do they take the order in which the events occur into account? Or alternatively, is it -by defnition- true that $P(A\cap B) = P(B\cap A)$ ? ...
0
votes
1answer
24 views

What is the values of the $P(a)$ and $P(b)$ here?

I am watching a video on EM algorithm here. It gives an example of how EM algorithm works. At first two Gaussian distributions are randomly given, and then by iterative calculations their parameters ...
0
votes
0answers
17 views

Confidence interval and probability mixed [closed]

An advertising agency needs to create a television advertisement for a sun block. The hirer, who makes this product, says that 40% of customers prefers his/her brand. The agency did a survey to verify ...
6
votes
1answer
85 views

Random variables with some properties (conditional expectation)

I am looking for two random variables which fulfills the following two things: a) $\mathbb E(X|Y)<\infty$ and $\mathbb E(Y|X)<\infty$ b) $E(X|Y)> Y$ and $\mathbb E(Y|X)>X$ a.s Here is ...
0
votes
1answer
72 views

which distribution should be used in this question?

A basketball player succeeds in making a basket three tries out of four. How many times must he try for a basket in order to have greater than 0.99 probability of making at least one basket? In this ...
0
votes
0answers
14 views

Meta analysis, joint posterior distribution of study effect

Meta analysis (with common study variation $\sigma$) often assumes that: $$ X_{i,j} | \theta_i \overset{ind}{\sim} N(\theta_i,\sigma)\\ \theta_i \overset{i.i.d.}{\sim} N(\mu,\tau) $$ where ...
-1
votes
1answer
28 views

Basic summation of conditional probabilities question

I read on Bishop Chap8 P 374 that: sum(P(b|c)P(c|a)) = P(b|a) where the sum is over c. Can you prove that?
7
votes
2answers
628 views

Why does convolution work?

So I know that if we want to find the probability distribution of a sum of independent random variables $X + Y$, we can compute it from the probability distributions of $X$ and $Y$, by saying $$f_{X ...
0
votes
0answers
39 views

How to determine the pdf from the sum of different distributions

Consider a discrete random variable $Z(t) = \phi_1Z(t-1) + \phi_2Z(t-2) +\dots+\phi_pZ(t-p) + \mu(t)$ $Y(t) = Z(t) + \eta(t)$ where $\mu$ is a zero-mean deterministic nonlinear signal following a ...
0
votes
0answers
22 views

Beta Binomial Distribution with a priori $\alpha$ and $\beta$ to Account for Probability Forecasts

I am trying to use a beta binomial distribution to calculate how much a single vote would count in a 2-choice election, given $n$ voters and a $p$ forecast: $ f(\lceil\frac{n}{2}\rceil;n,p) $ where $ ...
1
vote
1answer
34 views

nonparametric method to calculate the probability how alike two samples are

I have two samples with each couple of hunderd observations. I want to calculate a probabilty how much they look alike. I'm aware of tests like kolmogorov smirnov but I don't think I need this. I ...
-1
votes
1answer
51 views

Indepent variables and these functions [closed]

Random variables $x_1, x_2,...,x_n$ are independent. Then I want to show whether these functions $$y_1=f_1(x) \\ y_2=f_2(x) \\ ... \\ y_n=f_n(x)$$ are independent or not . How to prove this?
0
votes
1answer
21 views

Asking for help with a probability question for “learning dyadic data”

I am reading a paper "Learning from dyadic data" written by Thomas Hofmann, Jan Puzicha and Michael I. Jordan, which lays a foundation for a later paper that proposes the famous probabilistic latent ...