Binomial distribution with dependent trials?

In summary, the conversation discusses a problem involving a string with n characters and a probability p that each character is wrong. A sliding window of length k is used to determine the mean and variance of the number of moving windows without any error. The questioner suggests defining a discrete random variable to count the number of error-free windows, but it becomes difficult to count and a generating function is also considered. The total number of windows is n-k+1.
  • #1
Reynolds
1
0
Hi to you all!
I need your help with following problem:

String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, that slides over that string. For the given parameters p,k and n one must must determine the mean and variance of the number of the moving windows without any error.

For n = 5 and k = 2 we have sliding windows that contain letters of sting on positions 12, 23, 34 and 45.

I was thinking that I may define discrete random variable that counts how many windows are there without any error, but very soon it becomes quite difficult to count. I was also trying to define some sort of generating function, but i did not get far. Thank you in advance!
 
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  • #2
Your question is confusing. The number of windows is n-k+1. What are you trying to do?
 

1. What is a binomial distribution with dependent trials?

A binomial distribution with dependent trials is a statistical probability distribution that describes the probability of a certain number of successes in a fixed number of repeated trials, where the outcome of each trial is dependent on the outcome of previous trials.

2. How is a binomial distribution with dependent trials different from a regular binomial distribution?

A regular binomial distribution assumes independent trials, meaning the outcome of one trial does not affect the outcome of another. A binomial distribution with dependent trials takes into account the correlation between trials, meaning the outcome of one trial can impact the outcome of subsequent trials.

3. What is the formula for calculating the probability in a binomial distribution with dependent trials?

The formula for calculating the probability in a binomial distribution with dependent trials is P(x) = nCx * p^x * (1-p)^(n-x), where P(x) is the probability of x successes, n is the number of trials, and p is the probability of success in each trial.

4. Can a binomial distribution with dependent trials be used for continuous data?

No, a binomial distribution with dependent trials is only applicable for discrete data, meaning that the outcome of each trial is either a success or failure.

5. What are some real-world examples of a binomial distribution with dependent trials?

Some real-world examples of a binomial distribution with dependent trials include the success rate of a pharmaceutical drug on a specific medical condition, the probability of a student passing a series of exams given their performance on previous exams, and the likelihood of a sports team winning a series of games based on their previous performance against a specific opponent.

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