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Home » To determine which value maximizes \( C(x) \), evaluate the second derivative: - AMAZONAWS

To determine which value maximizes \( C(x) \), evaluate the second derivative: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Since X = sum of expected values over 3 selected communities:

📌 E[X] = 3 × 3 = <<3*3=9>>9.

📌 A robotics engineer programs a swarm of 10 autonomous inspection robots. Each robot independently detects a flaw with probability 0.8. What is the probability that at least 8 robots detect a flaw during a single inspection cycle?

📌 This is a binomial probability: n = 10, p = 0.8, find P(X ≥ 8) = P(X=8) + P(X=9) + P(X=10).

📌 P(X=k) = C(10,k) (0.8)^k (0.2)^(10−k)

📌 P(X=8) = C(10,8) (0.8)^8 (0.2)^2 = 45 × 0.16777216 × 0.04 ≈ 0.30199

📌 P(X=9) = C(10,9) (0.8)^9 (0.2)^1 = 10 × 0.134217728 × 0.2 ≈ 0.268435

📌 P(X=10) = C(10,10) (0.8)^10 = 1 × 0.1073741824 ≈ 0.10737

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