Changed case: a shared rate and a rare exit
Work outside the widget on two unfamiliar model changes. First, a pair of one-hour windows shares a hidden rate Λ: it is 0 or 4 per hour with equal probability. Conditional on the rate, the two counts are independent Poisson(Λ); rate zero means no events, not an Exp(0) sampler. Compare this with refreshing Λ independently in each window. Derive each one-window mean/variance, pair covariance and pair-zero probability, then propose a paired observation that distinguishes the constructions. Second, change the trapped route to A→B,C each with probability 1/2, B→B with probability 99/100 and B→D with probability 1/100. Derive eventual C/D probabilities, mean transitions and survival after an integer m≥1. Compute exact expressions for D-by-m and E[min(T,m)], and explain why many unresolved paths at m=64 do not prove nonabsorption. Contrast with setting the exit probability exactly to zero. Supply your own complete argument, cite assistance and preserve this response separately from the main manuscript.
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