# Tagged Questions

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

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### Product of Sums of Bernoulli variables

Let $x_1 \ldots x_a,y_1 \ldots y_b$ be independent random variables taking values $+1$ or $-1$ with probability 0.5 each. Consider the sum $S = \sum_{i,j} x_i\times y_j$. I wish to upper bound the ...
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### Conditional probability update for correlated Poisson variables

Some background: I am trying to estimate the number of failures in two related machine populations. I model machine failures in a year as a correlated Poisson process as such: $Y_0,\ Y_1$ and $Y_2$ ...
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### Marginal distribution of the diagonal of an inverse Wishart distributed matrix

Suppose $X\sim InvWishart(\nu, \Sigma_0)$. I'm interested in the marginal distribution of the diagonal elements $diag(X) = (x_{11}, \dots, x_{pp})$. There are a few simple results on the distribution ...
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### Probabilities from Logistic Regression

I have built a logistic regression model in R and though the result appears to be satisfactory to some degree, there is one question I have not be able to address. I am not sure if my approach is at ...
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### Distribution of the hyperbolic distance between random points in the Poincaré disc

Let two points at polar coordinates $(r_i, \theta_i)$ and $(r_j, \theta_j)$ be hyperbolic points in $\mathbb{H}^2_\zeta$ with curvature $K=-\zeta^2$. The radial coordinates of these points are ...
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### Combining evidence using Dempster-Shafer theory

Can someone post a simple explanation of Dempster-Shafer theory? There are lot of links available but the reading material in those sites is academic in nature and time consuming to read and ...
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### Estimating repeat shoppers from an incomplete sampling

I'm trying to estimate how many people visited the farmers market once, twice, thrice, etc. in a given time period, using sampled data. We have interview data from approximately 50% of visitors as ...
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### Visualizing probability of event over time, based on epoch time

I have a list of epoch/unix times at which an event happened. My hypothesis is that there are certain times during the week when this event might happen more frequently. How can I visualize/determine ...
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### How to pick from a set of random variables the one with the highest mean using a fixed number measurements?

Suppose we have $N$ approximately normally distributed continuous random variables $X_1, X_2, X_3, \ldots,X_N$, each with an unknown mean and variance. I'd like to find the random variable with the ...
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### How to predict the probability of a performance rank for a test taker on a future test based on previous test scores?

Four students sit a series of tests, each test contains 10 questions. Students are ranked 1-4 in each test depending upon who got the most questions correct. ...
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### Predicting time interval based on statistics

Let's say, we have some random event. We also have a hist of time intervals between two events, based on statistical data. For example, a frequency distribution: ...
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### Why does a finite, irreducible and aperiodic Markov chain with a doubly-stochastic matrix P have a uniform limiting distribution?

The theorem is "If a transition matrix for an irreducible Markov chain with a ﬁnite state space S is doubly stochastic, its (unique) invariant measure is uniform over S." If a Markov Chain has a ...
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### What is the difference between deterministic models and probabilistic models that assume that error follows a degenerate distribution?

I have thought for a while about this, and I'm not entirely certain what the difference is between a deterministic model and a probabilistic model with error following a degenerate distribution ...
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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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Suppose $y_1$, $y_2$, $\cdots$, $y_n$ are sampled from a normal distribution with expected value $\mu$ and variance $\sigma$. Then how to obtain the expectations and variances of the following ...
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### I want to show $e^{-\alpha t}B(e^{2\alpha t})$ is a Gaussian process and I find mean and covariance functions

Let $B(t)$ be Brownian motion. Show that $e^{-\alpha t}B(e^{2\alpha t})$ is a Gaussian process. Find its mean and covariance functions. thanks .
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### Expected value calculation BS2

I have great difficulty in calculating $\mathrm{E}\left(T_{1} T_{2}^{-1}\right)$ where $T_{i}$ is a random variable distributed according to the Birnbaum-Saunders distribution. Are there any ...
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### Degenerate random variable

Let $X$ and $Y$ be independent $rv$ such that $XY$ is a degenerate $rv$. Can I say that individually $X$ and $Y$ are also degenerate? Why? thanks..
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For bivariate zero-mean normal distribution $P(x_1,x_2)$, the quadrant probability is defined as $P(x_1>0,x_2>0)$ or $P(x_1<0,x_2<0)$ and according to ...
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### Bounding expected maximum of inner products

Let $x=(x_{1},\dots,x_{n})^{T}$ be $n$ dimensional random vector uniformly distributed over the $L1$ unit sphere. That is, all $x$ such that $\|x\|_{1} = 1$ have equal probability and all other $x$ ...
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### Combining evidence from different sources

I am computing similarities between words using similarity measures based on wordnet. I have obtained similarity measures for two words using three different methods - JNC (Jiang and Conrath), BNP ...
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### How to calculate the log likelihood in HMM from the output of the forward algorithm in R?

How can I get the log likelihood or the probability value from the forward algorithm for an observed sequence? For example, when I executed the forward algorithm in ...
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### A question regarding the central limit theorem

I would appreciate if you could please take a look at the following attempt. I am preparing for an upcoming exam, and this is taken from a past exam paper. I would like to know if it is correct. Thank ...