526 views

Dependent Bernoulli trials with same probability of success? [duplicate]

I am not that good at probability theory. My need: I need a simple example of a series of Bernoulli trials with the same probability of success in each trial, but where the Bernoulli trials are ...
• 15
1 vote
42 views

Generating correlated samples from bernoulli variables [duplicate]

I am trying to implement a program that samples from two identically distributed Bernoulli random variables, $X_1$ and $X_2$, such that they have a specific correlation coefficient, $\rho$. I found a ...
• 371
10 views

Help with calculating probility of outcomes between two correlated binary events [duplicate]

My google fu has failed me to find a method for this. I would assume there is a deterministed equation for what I'm trying to do but maybe it's more complicated than I am thinking. I have two binary ...
68k views

How to generate correlated random numbers (given means, variances and degree of correlation)?

I'm sorry if this seems a bit too basic, but I guess I'm just looking to confirm understanding here. I get the sense I'd have to do this in two steps, and I've started trying to grok correlation ...
7k views

How to generate correlated Bernoulli variables?

Suppose I want to simulate a survey variable in R which values derive from four binary cases $c_i$ with $i=\{1,2,3, 4\}$, each with it's probability $\Pr(c_i=1)=p_i$. Let's assume that the cases ...
• 878
3k views

How to generate Bernoulli random variables with common correlation $\rho$?

Suppose I want to generate $X_1, \ldots, X_n$ Bernoulli random variables such that: $$Corr(X_i, X_j) = \rho$$ for all $i \neq j$. I am wondering what method I might be able to use (I will be ...
• 4,418
4k views

Interpretation of correlation coefficient between two binary variables

I have a dataset with binary variables for mitigation measures (0= a measure is not implemented, 1 = a measure is not implemented). I now want to know how often a certain measure is put in place ...
• 53
3k views

How to generate 2 correlated Beta random variables

I was wondering if it might be possible to generate 2 correlated $\mathsf{Beta}$ random variables? In other words, I want to generate two Beta random variables which can be said to have come from two ...
• 4,036
3k views

How to get distribution of sum of dependent bernoulli variables [closed]

I have $N$ Bernoulli variables, $X_1,...,X_N$ and $X_i\sim B(1, \pi_i)$, $\pi$ is known for each $X_i$, and $Y=X_1+...+X_N$, now I need to get the destribution of $Y$. If $X_i$ and $X_j$ are ...
• 241
802 views

Range of probability for non-independent events

Suppose the probability of rain on day 1 is $p_1$ and probability of rain on day 2 is $p_2$. Then the probability of rain for the entire two-day period is $1-(1-p_1)(1-p_2)$, under the assumption that ...
• 3
1 vote
670 views

Simulating Correlated Categorical Data

I am trying to simulate "correlated categorical data". For instance, consider the following example: Suppose there are 10 players (p1, p2, ...p10) - each day, a random combination of these ...
482 views

Calculate the Probabilities of 2 Negatively Correlated Outcomes

How does one calculate the probabilities of 2 outcomes that are negatively correlated (A happens and B happens, A happens and B doesn't happen, B happens and A doesn't happen, neither A or B happen)? ...
• 111
127 views

Random walking with high synthetic correlation

My question is if there is a way to create two graphs that move one point up or down at a time in a random walk, and there will be a high [synthetic] correlation between them [example: 0.8 in Pearson'...