# Tagged Questions

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1answer
33 views

### Detect bias in subset of Bernoulli processes

I'm looking for advice on the best method to use to answer this question. General scenario: We have multiple testing machines A,B,C,D etc. each tests a identical randomly selected part and provides ...
1answer
44 views

### Using continuity correction for normal approximation or not?

Below is a question on a recent actuarial exam, Exam 3L of the CAS. I didn't know whether or not to use the continuity correction when using the normal approximation to do hypothesis testing ...
2answers
47 views

### Find the expected value of $(\bar X_n-p)^3$

Let $X_1,X_2,\dots, X_n$ be a random sample from a Bernoulli distribution with parameter $p$. Let $\bar X_n$ be the sample average given by $\bar X_n=\frac{1}{n} (X_1+X_2+\dots+ X_n)$). Find the ...
0answers
55 views

### Why is it futile to use the deviance as a goodness-of-fit measure for Bernoulli data?

In Ordinal Data Modelling by Johson & Albert, page 102-103: For Bernoulli observations [...] the asymptotic chi-squared distribution of the deviance statistic may not pertain. Indeed, for ...
3answers
133 views

### The probability of getting one variation of consecutive outcomes in Bernoulli trials before another

Consider tossing a fair coin and writing down the outcomes in a sequence of symbols. "H" stands for head and "T" for tail. Let A , B and C be the words HTHH , HHTH and THHH respectively. What is ...
0answers
9 views

### Using known correlations to select a sample that maximizes model prediction

I want to model the outcome of a binary dependent variable D over a large universe [many records, 100s of variables]. Given a fixed sample size, I want to maximize the accuracy of the model over the ...
1answer
85 views

### exponential density & bernoulli distribution

I had asked a question on Maximum Likelihood earlier. Now I have two questions that are related to this question which had: Let $x$ have an exponential density \$p(x|\theta) = \theta e^{-\theta x} ...
1answer
351 views

### Empirical distribution alternative

BOUNTY: The full bounty will be awarded to someone who provides a reference to any published paper which uses or mentions the estimator $\tilde{F}$ below. Motivation: This section is probably not ...
2answers
119 views

### How does the confidence interval for the parameter p of a bernoulli trial vary with the value of p itself?

This is a very basic question (I'm currently studying undergrad level statistics), but I was hoping for some clarification regarding an assertion I read in a newspaper article earlier today. The ...
2answers
94 views

### Flipping random coins from a bag - equivalent to a single coin?

My first and I think naive question here. I am trying to model a certain business, and the simplest model I am willing to test is: 1. there is a bag of differently biased coins. 2. every step, a ...
1answer
94 views

### Compute a confidence interval for Bernoulli distribution

Given a Bernoulli distribution with a success probability of p = 0.02. Let's say we have N=3000 samples. How can I compute a confidence intervals for the expected number of successes (e.g., with 5% ...
2answers
138 views

### Dependent Bernoulli trials

The probability of a sequence of n independent Bernoulli trials can be easily expressed as $$p(x_1,...,x_n|p_1,...,p_n)=\prod_{i=1}^np_i^{x_i}(1-p_i)^{1-x_i}$$ but what if the trials are not ...
0answers
56 views

### What do I need to know about Bernoulli distributions to build a Naive Bayesian classifier?

I'm building a naive bayesian classifier for a binary classification. Right now I have an estimator for Bernoulli distributions, and real distributions (using a kernel mixture distribution). I can ...
0answers
90 views

### Wilson's confidence interval for standard deviation?

I have a a set of films, and for each films, a set of reviews - varying between 1 review and several hundred reviews for each film. Each review has a star rating from 1 to 5. I am using Wilson's ...
1answer
162 views

### How to show operations on two random variables (each Bernoulli) are dependent but not correlated?

I was looking at the following question from "One Thousand Exercises in Probability" by Grimmett, page 25, question 16 (not homework just self-study): Let $X$ and $Y$ be independent Bernoulli ...
1answer
121 views

### Testing median, and distribution of Binomial

Given the median is $m>0$ We have $n$ random variables: $Y_1,Y_2,..,Y_n$ If we observe a value above $m$ then $Y_i=1$ if we observe a value below $m$ then $Y_i=0$ The probability of getting an ...
3answers
289 views

### K successes in Bernouli trials, or George Lucas movie experiment

I'm reading "The Drunkard's Walk" now and cannot understand one story from it. Here it goes: Imagine that George Lucas makes a new Star Wars film and in one test market decides to perform a crazy ...
1answer
156 views

### Calculating standard error for a Normal population

I'm a programmer, with a decent but not-expert knowledge of stats, and I'm working through these instructions for how to create funnel plots. I understand from a previous question that the standard ...
2answers
696 views

### Expectation of a product of multiple random (Bernoulli) variables

I'm doing a research and using random variables to model a random process. I'm defining a Bernoulli random variable as a product of several other Bernoulli variables (three or more). So, I have the ...
1answer
106 views

### Basic information or texts required about modelling k bernoulli trials

I have been presented with a dataset comprised of individuals and the number of teeth they have had extracted. The maximum is 32, and almost half of the data are zeros. I have been asked to suggest an ...
1answer
101 views

### A function of Bernoulli variables?

Let $X_1,X_2,...,X_n$ be a fixed number of Bernoulli random variables. My problem is to find a distribution for $Y$ such that for some function $f$, we have $Y=f(X_1,X_2,...,X_n)$. There are two ...
1answer
96 views

### Why is the expected value of the number of trials before the first success larger than the number of trials with a 50% probability of success?

For a Bernoulli distribution with parameter p, the number of trials with a 50% probability of at least one success is about (1/p) * ln(2). But the expected value of the corresponding geometric ...
1answer
104 views

### Expected value of this Jackpot game [closed]

If there exists a fair National Lottery, that someone bets £1, Jackpot increases by £1, and there is p chance that he wins a Jackpot. If a Jackpot is won, it is reset to 0. repeats. We can easily ...
1answer
88 views

### What is distribution of lengths of gaps between occurrences of ones in Bernoulli process?

Which distribution fits the following data? Data are generated by the process: $X_t, \, t=1,2,3,\ldots,n$ is equal 1 with probability $p$ and 0 with probability $(1-p)$ for each $t$. What is the ...
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