adbd_with_noise - 50 ^ 40 3^ 30 20 10 0 0.8 0.9 a ^d 1 1.1...

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0.8 0.9 1 1.1 1.2 0 10 20 30 40 50 ˆ a * d σ ˆ μ Figure 5: Histogram of the estimated a d ’s. Estimated mean μ = 0 . 996408 and estimated standard deviation σ = 0 . 057748. Suppose E Δ = { ˆ a * d < 1 } . recall ( a d = e aT ) We can estimate P ( E ), the probability of E from the simulation data as : ˆ P ( E ) = Number of experiments in which the event occurs Total number of experiments
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adbd_with_noise - 50 ^ 40 3^ 30 20 10 0 0.8 0.9 a ^d 1 1.1...

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