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

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Can you show that $\bar{X}$ is a consistent estimator for $\lambda$ using Tchebysheff's inequality?

This question was taken from a practice exam in my statistics course. Given a random sample $X_1, X_2, ... X_n$ from a Poisson distribution with mean $\lambda$, can you show that $\bar{X}$ is ...
-2
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2answers
17 views

Probability of two different players scoring a goal

Bookmakers quite often price players to score a goal at any point during the game. For example, they may give Ronaldo a 52% chance of scoring a goal in a game, and Messi a 60% chance of scoring a ...
3
votes
1answer
41 views

Gamma Distribution and Life of Component?

I came across an old exam question as follows: If the life of one computer component (in years) has Gamma distribution with mean $6$ and variance $18$, how can we find the probability that this ...
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1answer
20 views

Resampling probability

I have a population of n unique items and am taking a sample of r. I am sampling with replacement. I would like to calculate the probability of sampling any specific item x times give the sample size ...
1
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1answer
14 views

Hypothesis Test on Contest, a problems?

We have a contest 1 weeks ago. One question is a bit strange for us as follows: $X\sim B(4,p). $ for test $H_0:p=0.2$ versus $H_1:p>0.2$. if $X=4$, $H_0$ assumption is rejected. calculate ...
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0answers
15 views

Relationship between Poisson and Exponential distribution problem

I'm struggling to understand why I can't use an exponential distribution to solve this question: Astronomers treat the number of stars in a given volume of space as a Poisson random variable. On ...
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0answers
16 views

statistics question [on hold]

An event planner does research and finds that approximately 2.75% of the people in the area where a large event is being held are pescatarian. Treat the 250 guests expected at the event as a simple ...
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0answers
16 views

transform probability density function [on hold]

I have the numeric values to plot a probability density function....they look like ...
-2
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0answers
27 views

University of London Past Paper help [on hold]

Hey this is my third year trying to pass my stats exam, I simply have a bad block when it comes to statistics and need some help. I'm trying to do a 2014 past paper and so far the only thing i can do ...
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0answers
6 views

relationship between power means and population zscore calculations

Can one use a power mean of the ages in a room to determine the age break down of a room? Let's say you have a room full of people, by using the average age and standard deviation of the age, how do ...
3
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1answer
206 views

How to generate a specific number of random binaries with probablities proportional to given values?

I have such a matrix in an excel sheet. It has 140 cells. I want to generate 20 binaries randomly. However, the probability of generating "1" in each cell is proportional to cell's value. Namely, ...
0
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0answers
10 views

how can I save the survival probability that used to calculate NRI for an indiviual?

I am trying to save the survival probability that used to calculate NRI (i.e. in the survIDINRI package) for an individual. and I wanted to use these probabilities to further analyse what kind of ...
0
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1answer
38 views

How can we find $Cov(X(s), X(t))$ for a compound poisson process?

If I assume that $X(t)$ is a compound poisson process, how can it be found what $Cov(X(s), X(t))$ is? I have seen this over and over in books, but they only state it as fact. It is stated to be ...
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2answers
36 views

Expected number of trials

Consider independent trials, each of which is a success with probability p and derive the expected number of trials needed to obtain k consecutive successes by (a)conditioning on the time of the ...
0
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1answer
35 views

Uniform with dependent parameters

I was helping a student with a question I couldn't solve. We have the following process: X is sampled from a $U(0,1)$ distribution. Then Y is sampled from a $U(-x,x)$ distribution. Therefore I have ...
3
votes
1answer
47 views

PyMC3 Implementation of Probabilistic Matrix Factorization (PMF): MAP produces all 0s

I've started working with pymc3 over the past few days, and after getting a feel for the basics, I've tried implementing the Probabilistic Matrix Factorization model. For validation, I use a subset ...
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0answers
38 views

CDF of sum of 3 independent discrete uniform random variables on {1,2,…,n}

What is an approximate closed formula for this probability, with a derivation: p(k,n) is the probability, that among $n$ PC discs and $k$ errors in sum on them, there will be at least $1$ disc ...
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29 views

Conditional Probability [on hold]

Let $X_1,X_2,X_3$ be a sample of size $3$ from the Bernoulli distribution . Consider the statistic $S=s(X_1+X_2+X_3)$ . To show that $S$ is sufficient statistic , it is written that ...
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0answers
18 views

Bad regression predictions with probability values

I have to pull through a regression on a set of probabilities (so values between 0 and 1). Those probabilities are related to a binary variable, which I have to forecast exactly. My code basically ...
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0answers
23 views

linear regression and plausibility of forecast

Does there exist any mathematical model where the plausibility for a forecast of the dependent variable by linear regression could be expressed. E.g. in terms of any laboratory parameter measured and ...
2
votes
1answer
120 views

Deriving Density Function (pdf) from Distribution Function (cdf)

A random variable $V$ has the distribution function: $$ F(v) = \begin{cases} 0, & \text{for $v<0$ } \\ 1-(1-v)^A, & \text{for $0\le v\le1$ } \\ 1,& \text{for $v>1$ } \\ \end{cases} ...
3
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1answer
44 views

What allows us to write $P(T_2 >t) = E[P(T_2 >t)| T_1] $

I am currently working with a time process, $T_1, T_2, ..$. I saw in an associated paper that $P(T_2 >t) = E[P(T_2 >t)| T_1]$. I wasn't sure what property allowed me to do this as it appears ...
3
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1answer
44 views

Significance of $1$ in the model: $Y_i=1[B_0+B_1X_i\geq \epsilon_i]$ in Binary Choice Model?

I'm having a bit of trouble understanding exactly why there is a "1" in the general simple Binary Choice Model where $Y_i$ can take a value of either $0$ or $1$. We also assume that the conditional ...
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0answers
38 views

Question about the departure process of a M/GI/$\infty$ queue

Consider an $M/GI/ \infty $ queue with the following service time distribution: the service time is $1/\mu_i$ with probabbility $p_i$, and $\sum_{i=1}^kp_i=1$ and $\sum_{i=1}^kp_i/\mu_i=1/\mu$. In ...
2
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0answers
19 views

EM algorithm: With prior vs. not prior

I have a working EM algorithm without prior. I am asking for some advice on how to add prior on latent variables. Define: $t_i \in \{ +1, -1 \} $: variables of interest to be predicted $p_j \in ...
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0answers
11 views

What is inference, training and testing in Undirected Graphical Model?

I have a Undirected Graphical Model (UGM) - $ \sum_i w_i\phi_i $ . What is the inference and training here? Suppose I have a train data and test data how do I train and test using this data and UGM? ...
5
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1answer
45 views

Closed form for $\mathbb{E}[\ln (1-p)]$, for $p \sim Beta(\alpha, \beta)$

We know that if $p \sim Beta(\alpha, \beta)$, then $$ \mathbb{E}[\ln p] = \psi(\alpha) - \psi(\alpha + \beta) $$ where $\psi(.)$ is the Digamma function. Is there an easy form for $ \mathbb{E}[\ln ...
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0answers
28 views

SVM output to probabilistic affiliation

How can I convert the svm output for multiple class classification(one vs one approach) to probabilistic values? Meaning that I want to have a probability for a tested element to be in each available ...
-2
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1answer
43 views

Help with HW questions

I have two following questions I could not really decipher how to get the P-Value. Data from a recent year showed that 71% of the tens of thousands of applicants to a certain program were accepted. ...
3
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0answers
40 views

By how much the mean and variance in size of beans changes after sampling with replacement?

You have a bag of $n$ beans of different sizes. The mean and standard deviation of the size of these beans is $\mu_1$ and $\sigma_1$ respectively. The probability of drawing a bean is an increasing ...
2
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1answer
299 views

Expected number of dice Rolls require to make a sum greater than or equal to K?

A 6 sided dice is rolled iteratively. What is the expected number of rolls required to make a sum greater than or equal to K? Before Edit ...
0
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1answer
347 views

Why probability distribution function gives “~.40” probability when it should have been 1.0? [duplicate]

I am following code given here- http://www.bigdataexaminer.com/how-to-implement-these-5-powerful-probability-distributions-in-python/ Under "Normal Distribution" section, the graph peaks at .40 when ...
2
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0answers
32 views

Calculate the probability mass function of the new random variable $Z≡X+Y$

I am having trouble with these. How do I complete the table? Consider the random variables $X$ and $Y$ with joint distribution as given below. ...
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0answers
17 views

Estimating class probabilities given discriminative functions per class

What is the effective way to estimating class probabilities per class, if I know discriminative functions for each class (I have trained ML models giving some scores). My naive implementation is to ...
3
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1answer
83 views

Indicator Function

Here is an excerpt from "All of Statistics" by Larry Wasserman (page 23): Given an event A, define the indicator function of A by $$ I_{A}(\omega)= \color{Red}{I(\omega \in A)} ...
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33 views

What's in a family [closed]

So PM David Cameron and Kim Kardashian are 13th cousins. What is the probability that they actually share at least one gene from their common ancestor?
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0answers
13 views

weighting of aligned subsequences by their length

I have a pool of subsequences, each one associated with a probability (and other properties that you don't need to know) that quantifies how frequently that subsequence occurs. In order to select ...
2
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1answer
538 views

What is the probability that a sequence of events completes within a given time interval?

If an event has probability p of occurring in some time interval, then the probability the event does not occur q is: $$ q=1-p $$ The probability of the event not occurring by time t will be: $$ ...
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0answers
14 views

psychic testing control group

You have seen it on television, two men sit across a table from each other, a deck of cards between them. The man in a lab coat draws a card and looks at the card. The other man places his hand to his ...
0
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0answers
15 views

Can you have a “partial death” event as censored variable in survival analysis?

I am working on a dataset in which most of the patients encounter 'partial' death(the variable is in the range[0,1]) before censoring happens. Currently, I applied a proportional hazard model by ...
0
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0answers
21 views

How to estimate coin probability after successive tosses

I want to estimate the distribution of faces of a coin. Initially, we believe in the equal likely of both side occurrence, that $\Pr(head) = \Pr(tail) = 0.5$ Then we toss: The first time we toss, we ...
3
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1answer
81 views

How to compute the pdf analytically for the sum of generalized gamma

Question: problem statement $$z^d = \sum_i x_i^d $$ pdf of $X = \frac{d(\lambda x^d)^n}{x \Gamma(n)} \exp(-\lambda x^d)$ which is a generalized Gamma distribution and they represent euclidean ...
8
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1answer
76 views

Probability of a consecutive pair of values

Lets $X=(x_1, x_2,...x_{20})$ where $x_i\sim N(0,1)$ and $x_i, x_j$ are independent $\forall i\neq j$. What is the probability to obtain a sample $X$ where there are at least two consecutive values ...
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1answer
47 views

Identify the distribution

Can anyone tell me which distribution has the density $$f(x)=\frac{x}{\sigma ^2}e^{-\frac{x^2}{\sigma ^2}}I(0,\infty)(x),\sigma >0$$
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14 views

Find the mean of lognormal rv's with available variance and the sum of rv's

I have the sum of a bunch of random variables $S$, v = [1 1 2 2 3 3 4 ...]; S = sum(v); I know that vector $v$ is lognormally distributed, BUT I DON'T KNOW IT. ...
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0answers
32 views

How likely is it, that a value belongs to a given distribution?

I'm struggling with this question: I created 100 random data sets and the results are normal distributed. This data will be my null hypothesis. Now I want to check, if an observed value belongs to ...
4
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1answer
36 views

How is softmax unit derived and what is the implication?

I'm trying to understand why the softmax function is defined as such: $\frac{e^{z_{j}}} {\Sigma^{K}_{k=1}{e^{z_{k}}}} = \sigma(z)$ I understand how this normalizes the data and properly maps to some ...
3
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1answer
217 views

I have an epidemiology question with logs

I am a graduate student in biochemistry working on cancer. I am currently looking at epidemiology models of the disease. Epidemiologists have developed formulas that predict the frequency of various ...
2
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0answers
68 views

a question on 0-1 valued stochastic process [closed]

Consider a stochastic process $X_{t}$ taking values in the set $\{0,1\}$ according to the probability measure $\mu$. Let $$Y_{t} = \mu\left(\limsup_{T \rightarrow \infty}\frac{1}{T}\sum_{t = 0}^{T - ...
2
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0answers
20 views

Bayes Rule with 1 Signal but 2 Unknowns

This is a question I originally posted in the math.stackexchange site, but didn't get much of an answer. Suppose I have an unknown variable $X_i = \alpha_i + \beta_i$ where $\alpha$ is one of 2 ...