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math-340:m340-f15-hw:hw-17 [2015/10/20 05:36]
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math-340:m340-f15-hw:hw-17 [2015/10/20 05:36] (current)
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   - $E(X) = 200000 \cdot \dfrac{1}{10000} = 2$   - $E(X) = 200000 \cdot \dfrac{1}{10000} = 2$
   - $P(X = 0) = (0.9999)^{20000} = 0.135322$, $P(X = 1) = 20000 \cdot (0.0001) \cdot (0.9999)^{19999} = 0.270671$, $P(X = 2) = \binom{20000}{2} \cdot (0.0001)^2 \cdot (0.9999)^{19998} = 0.270684$, $P(X > 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) = 0.1428675$   - $P(X = 0) = (0.9999)^{20000} = 0.135322$, $P(X = 1) = 20000 \cdot (0.0001) \cdot (0.9999)^{19999} = 0.270671$, $P(X = 2) = \binom{20000}{2} \cdot (0.0001)^2 \cdot (0.9999)^{19998} = 0.270684$, $P(X > 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) = 0.1428675$
-  - Using the Poisson approximation for binomial probabilities,​ $P(X = 0) \approx e^{-2} = 0.135335$, $P(X = 1) \approx 2e^{-2} = 0.270671$, $P(X = 2) \approx \frac{2^2 \cdot e^{-2}}{2} = 0.270671$, $P(X > 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) \approx 0.1428765$+  - Using the Poisson approximation for binomial probabilities,​ $P(X = 0) \approx e^{-2} = 0.135335$, $P(X = 1) \approx 2e^{-2} = 0.270671$, $P(X = 2) \approx \frac{2^2 \cdot e^{-2}}{2} = 0.270671$, $P(X > 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) \approx 0.1428765$