This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revision | Last revisionBoth sides next revision | ||
math-340:m340-f15-hw:hw-17 [2015/10/18 17:41] – dcs | math-340:m340-f15-hw:hw-17 [2015/10/20 05:36] – dcs | ||
---|---|---|---|
Line 16: | Line 16: | ||
- $E(X) = 200000 \cdot \dfrac{1}{10000} = 2$ | - $E(X) = 200000 \cdot \dfrac{1}{10000} = 2$ | ||
- | - $P(X = 0) = (0.9999)^{20000} = 0.135322$, $P(X = 1) = 20000 \cdot (0.0001) \cdot (0.9999)^{19999} = 0.270671$, $P(X = 2) = \binom{20000}{2} \cdot (0.0001)^2 \cdot (0.9999)^{19998} = 0.270684$, $P(X > 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) = 0.323324$ | + | - $P(X = 0) = (0.9999)^{20000} = 0.135322$, $P(X = 1) = 20000 \cdot (0.0001) \cdot (0.9999)^{19999} = 0.270671$, $P(X = 2) = \binom{20000}{2} \cdot (0.0001)^2 \cdot (0.9999)^{19998} = 0.270684$, $P(X > 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) = 0.1428675$ |
- | - Using the Poisson approximation for binomial probabilities, | + | - Using the Poisson approximation for binomial probabilities, |