## Binomial distribution with dependent trials?

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### Binomial distribution with dependent trials?

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 with out 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!