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Thread: Calculating probabilities in parallel recurring sequences

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    Calculating probabilities in parallel recurring sequences

    I am working with certain recurring sequences in genetics and try to calculate certain probabilities:

    Let for instance
    $\displaystyle $$\langle g_i\rangle :=\{1,1,1,6,1,1,1,6,...,1,1,1,6\}$$ $ and
    $\displaystyle $$\langle h_i\rangle :=\{1,1,1,1,6,1,1,1,1,6,...,1,1,1,1,6\}$$$

    be to recurrent chains of identical length $\displaystyle $i_{\max}=20$$

    How can one calculate the probability that at a certain selected index $\displaystyle $i_*$$ we would have on both chains a $\displaystyle $1$$, i.o.w.:

    $\displaystyle $$\langle g_{i_*}\rangle =\langle h_{i_*}\rangle =1$$$

    to explain further the expansion of the problem...
    let $\displaystyle $\langle a_{i,m} \rangle$$ be $\displaystyle $m$$ recurring sequences (in above example $\displaystyle $m=\{1,2\}$$) each with different frequencies of recurrence $\displaystyle $f_m$$ (above example $\displaystyle $f_m=\{4,5\}$$) and the identical entrained length of $\displaystyle $L=\prod_{m}f_m$$.
    How can I calculate the probability that (only) the 1s (the digits 1) of all $\displaystyle $m$$ chains would be compatible?
    Last edited by Hwarazmi; Apr 13th 2013 at 04:49 AM.
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