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I have two sequences of binary trials chosen at random. In both cases, $n$ is the length of the sequence, and $p$ is the success probability. Obviously, the sequences will not be identical, for example

$$A = [1,0,1,1,0,1,...]$$

$$B = [1,1,0,1,1,0,...]$$

What I want to find is the expected proportion of trials that match at each position (e.g. $A_x = B_x$). In other words on average, what percent of the trials in $A$ will match the corresponding trial in $B$?

electroducer
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1 Answers1

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$M=[1,0,0,1,0,0,\dots]$ on base of $M_x=1$ if $A_x=B_x$ and $M_x=0$ otherwise.

Again binomial and $\Pr(A_x=B_x)$is the success probability, corresponding with the percentage you mention.

Can you find that yourself?

drhab
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