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

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1answer
11 views

Conditional probability in random variables [on hold]

Let the time (in hours) needed to repair a broken car be a continuous random variable $X$. Then, in the case of $a$ and $b$ being two positive numbers and $b$ > $a$, would the following two problems ...
1
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1answer
52 views

What is a good way to model this set of time-series data? What might the distribution be? (Personal expenses)

I'm trying to make some sense out of this data, but have been having some trouble. The data is of personal expenses made during the last 90 days. How would one go about the modeling this type of data? ...
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0answers
11 views

Optimization of a non homogenous poisson process with unknown intensity distribution

Customers arrive at a bank counter according to a non-homogenous Poisson process with rate parameter $\lambda_k$. The service time at the counter is exponentially distributed where $\lambda_k$ and ...
0
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0answers
46 views

Conditions to be in a class of Poisson distribution

Ambulance cars are arriving at a traffic signal in accordance to a Poisson process. The arrival rate of ambulance cars is measured at every 1 hour. $\lambda_k$ is defined as $k_{th}$ hour arrival ...
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0answers
20 views

Predict number of users

I have a pretty basic question, but am pretty far removed from stats and modeling. I have historical data (daily, weekly, monthly, however I want to slice) for a few years and I want to predict the ...
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0answers
50 views

Statistic to use to measure intersection probability in set of elements

Being two sets of elements: set a: ele1, ele2, ele3, ele4, ele5, ele6, ele7 set b: ele3, ele4, ele8, ele9 And is intersection: ...
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1answer
20 views

Possible to estimate distribution around mean given #samples, mean, highest and lowest?

For a project for which there are multiple bidders, the following is known: Number of bidders: 24 Mean bid: 104 Highest bid: 356 Lowest bid: 20 Given the above, is it possible (however roughly) ...
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0answers
24 views

What are the practical problems where the prior and posterior probabilities derivable from data are not reliable?

In Rough Baysian Model (Rough sets and Bayes Factor), authors always say that this model is very applicable to practical problems where the prior and posterior probabilities derivable from data or ...
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2answers
62 views

Probability distribution of $aX + b$, where a and b are integers and $X$ is a uniform variable

My textbook has the following introductory example about functions of random variables: Suppose that $X$ is a random continuous variable with a uniform distribution over the interval $(0,1)$. ...
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0answers
20 views

How to combine posterior probabilities from different classifiers?

I have four different images $(X_1, X_2, X_3, X_4)$ which I classify with four different discriminate probabilistic models (discriminative classifiers) to obtain posterior probabilities of a pixel ...
1
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0answers
20 views

Perceptron Learning Algorithm: what is the probability that the viewed data is linearly separable, after some number of steps?

My understanding is that the PCA: will not converge if the data is not linearly separable might take exponentially many iterations, even if the data is linearly separable I'm wondering if, after ...
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1answer
49 views

What is the distribution of the maximum of two random integers chosen from [1,n]?

Suppose we have the set of integers from 1 to n. We proceed to choose two integers from this set at random and denote S = maximum of these two integers. What is the distribution of the random variable ...
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0answers
15 views

taking decisions: how to combine scores from different systems?

I have several completely different software components that are producing scores for certain candidate solutions. Now, setting aside the technical details of what is the problem that I want to solve ...
0
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1answer
56 views

Normal Distribution

I am a little bit confused about the correctness of the following statement. Could you check please, if my small "proof" is correct? Let $X_{1}, \ldots, X_{n}$ be a i.i.d sequence that follows a ...
0
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1answer
47 views

Central Limit Theorem Equation

I was wondering what the difference is between $Z_n=\frac{S_n-n\mu}{\sigma \sqrt{n}}=\frac{X_1+\ldots+X_n -n\mu}{\sigma \sqrt{n}}$ and $Z_n=\frac{X-n\mu}{\sigma/\sqrt{n}}$? What is the benefit of ...
0
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0answers
13 views

Visualize Sensitivity Results Using Combinations of Means and Standard Deviations of Two Normally Distributed Variables

I ran a sensitivity of my model, sampling the response space using two normally distributed variables. I used four nested repetition loops to generate this data, recording the average output of the ...
3
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3answers
518 views

Probability that the minimum of a normal random sample will exceed the maximum of another?

I sample independently $n$ data points following normal distribution with $\mu = 0$ and $\sigma = 1$. Then I divide the sample into two groups $G_1$ and $G_2$ of sizes $g_1$ and $g_2$ respectively ...
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0answers
29 views

Variation of the Coupon Collecting Problem

Suppose you are collecting coupons from a pool of 50 distinct types. These types can be divided into 10 sets of 5 types each. What is the expected number of coupons you need to collect in order to ...
0
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1answer
40 views

Test to determine observed vs. expected (not Chi-square)

I will work through how and what type of data I am getting before I ask my question: I made some code in R that flips n fair coins x times, and sums the number of successes (heads = 1, tails = 0) I ...
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0answers
35 views

Probability in the game Risk? [duplicate]

I've been playing a board game called risk lately, and I'm very interested in the probability behind it. Sorry if this question is it the wrong category, but I assumed that it was largely statistical. ...
0
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0answers
28 views

probability distribution of complex Gaussian column vector and conditional probability of complex Gaussian column vector

I have column vector $\vec r=[r_1\ r_2]^T$. $$\vec r =hA\vec s +\vec n$$ where $h$ is a complex number , $\vec n \sim \mathcal{C} \mathcal{N}(\begin{bmatrix} 0 \\ 0 ...
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1answer
56 views

Why don't log-likelihoods lead to log(0)?

I seem to oscillate between understanding this and not understanding this (which most likely means I've never understood it), but how do log likelihoods function in practice? I mean, when you take ...
0
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1answer
41 views

What does “asymptotically proportional” mean?

I am reviewing a paper that uses the term "asymptotically proportional" in a definition of a PDF. Unfortunately I can't find what this term precisely means. Can anyone fill me in?
4
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1answer
85 views

Minimum number of people such that 2 can be expected to sit next to each other

We are given a large, round table with $n$ seats. It is easy to see that whenever $p\geq \text{int}(\frac{n}{2}) + 1$ people are seated, at least $2$ people will sit next to each other (here ...
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0answers
23 views

Lorentz and Gaussian

I would like to ask the difference between Lorentz and Gaussian. In laser application, the intensity of Natural and Doppler broadening is different in a mathematical way simply due to the differences ...
1
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1answer
25 views

Equivalence of the dt and pt function in R

in my own curiosity I decided to question the equivalence of dt and pt in R. pt denotes the cumulative density function of the t-distribution. So this gives us $P(X \le x)$. So if I want to find the ...
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2answers
70 views

Particle filter for estimation of static parameters

I am considering particle filtering methods for the estimation of static and dynamic parameters. For the static parameters $\theta$, Liu and West (page 7, equation 3.1) describe an "artificial" ...
0
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1answer
48 views

The squared-norm of the projection of a Gaussian vector onto an independent $d$-dimensional subspace is a $\chi^2_{2d}$

How we can prove that: The squared-norm of the projection of a $N$-dimensional complex vector with i.i.d. unit-variance and zero mean Gaussian components onto an independent $d$-dimensional subspace ...
4
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1answer
154 views

Calculate mean and variance of a distribution of a distribution

I am using hierarchical distributions, of the following form: $\theta\sim N(\mu,\sigma)$ $\mu\sim N(a,b)$ I can calculate the mean, and variance using Mathematica, and find: $\mathrm{E}(\theta)=a$ ...
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0answers
24 views

Confidence intervals for estimates generated from a non-probability sample?

From what I understand, to generate a margin of error to have confidence intervals for a given estimate one needs the standard error of the estimate (SE). For the SE one needs information about the ...
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0answers
22 views

Calculating probability of sale from auction data

I have some data representing the last 6 months of closed auction data from a particular website. The data I have includes market value of product, actual sale amount, and date sold. I have about 600 ...
4
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2answers
589 views

Can someone tell me how to read this equation in words?

$$ P\left[\frac{\text{MTBF}\cdot2r}{\chi^2_{1-\alpha/2,2(r+1)}} \le \text{True MTBF} \le \frac{\text{MTBF}\cdot2r}{\chi^2_{\alpha/2,2r}} \right] \ge 1-\alpha $$ Can someone please help me to ...
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1answer
30 views

How to prove the identifiability of a likelihood

Consider the likelihood function for parameter vector ...
3
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1answer
114 views

Proof of Simplification of Conditional Expectation of Product of Random Variables

Could someone please provide detailed steps to prove or disprove the following? $E[XY\mid XY>k] = E[XE[Y\mid XY>k]]$ Here, $X,Y$ are independent random variables that could be discrete or ...
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0answers
27 views

Probability to be the millionth customer (What Would You Do?)

I saw this episode of "What Would You Do?" a few months ago, and I keep wondering what would statistically be the best thing to do in this situation. Here is the problem formulation: You are waiting ...
0
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1answer
22 views

Proof that Conditional Expectation of Sum is Sum of Conditional Expectations

\begin{eqnarray*} E\left[\left.\left(X+k\right)\right|\left(X+k\right)>0\right] & = & E\left[k\left|\left(X+k\right)>0\right.\right]+E\left[X\left|\left(X+k\right)>0\right.\right] ...
3
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3answers
97 views

How well does a single data point fit a distribution?

I have to come up with a way to measure the 'quality' of a distribution for a research project. We collect data over a a period of time $t_0$ through $t_1$ and then estimate the distribution that ...
0
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0answers
15 views

is there any R package for calculating transition probabilities for multi order markov chain?

I need to estimate the transition probabilities of a user whose k recent selections were x1, . . . ,xk and will select the item x' next. I know to calculate first order transition probabilities but ...
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0answers
10 views

Probabilistic models - clarification on separation of model and solver

Almost all of the material I read on probabilistic models/ probabilistic programming mentions separating solver and the model, thus stating the benifit that the model can be changed by the user ...
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1answer
31 views

Independence of random variables after a transformation

We are given four random variables $S:=(S_1,S_2,S_3,S_4)$ defined on $(\Omega, \mathcal A,P)$. The random variables can be viewed as being extracted from a stochastic process. I assume that all ...
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1answer
79 views

Find standard deviation of arbitrary game with multiple payouts

This earlier question asked how to get a 5.76 standard deviation for a single number bet on Roulette. The answer gave the formula, but unfortunately, the formula doesn't easily generalize to more than ...
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1answer
190 views

How many distributions are in the GLM?

I've identified multiple places in textbooks where the GLM is described with 5 distributions (viz., Gamma, Gaussian, Binomial, Inverse Gaussian, & Poisson). This is also exemplified in the family ...
0
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1answer
26 views

How to generate probability function for uncertain data based on euclidean distance?

I am calculating pairwise distances between some points. The obtained distances can either be accurate, over-estimated or under-estimated. The respective probability is 80%, 5% and 15%. And the error ...
1
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2answers
162 views

relation between probability and probability density function

According to this link: PDF To translate the probability density $ρ(x)$ into a probability, imagine that $I_x$ is some small interval around the point $x$. Then, assuming $ρ$ is continuous, the ...
0
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2answers
68 views

Median of ratio of independent variates with Beta distributions

Let $X, Y$ be independent random variables where $X \sim Beta(\alpha_1,\beta_1)$, $Y \sim Beta(\alpha_2,\beta_2)$, and $Z = X/Y$. Recall $X, Y$ are supported on $(0,1)$, so $z > 0$. I've ...
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1answer
84 views

Proof for Simplifying Integral involving Gaussian and Error Function

How do we simplify this integral? \begin{eqnarray*} \int_{-\infty}^{\infty}\left\{ ...
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0answers
40 views

Comparing likelihoods from non-nested models

Short: I have a series of joint probabilities (likelihoods) for how likely sample $Q$ belongs to group $K$. I need to compute a p-value describing how "significant" the "top" group is compared to ...
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0answers
39 views

When does it make sense to fit a distribution to data?

More in general, if a fitted generative model is at best a biased approximation, and let's say we're interested in the predictive distribution, there is always an information loss associated with the ...
0
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1answer
34 views

How do I obtain the uncertainty of a value generated from a known distribution?

I wish to semi-randomly generate values from the known distribution of a particular quantity. The distribution is represented in my data as a list of values with a probability for each value, where ...
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0answers
28 views

click through rate stats

I have a group of 10 users. Each user receives a daily notification for one week. Ideally, each user will click on all notifications received. At the end of the week I collect the number of clicks per ...