Introduction to Probability · 免费预览
大数定律
平均值向均值的收敛：由切比雪夫不等式证明的弱大数定律、几乎必然收敛的强大数定律，以及蒙特卡洛原理。
1. Averages settle
Averages settle
2. Weak versus strong
Weak versus strong
3. Monte Carlo and the long run's meaning
Monte Carlo and the long run's meaning
4. What the weak law states
The weak law of large numbers concludes what about the sample average?
5. Reading the strong law correctly
Which statement is the strong law's?
6. Averaging halves the error slowly
A Monte Carlo estimator has standard deviation 0.1 at n = 10000. At n = 40000, four times as many samples, the standard deviation is what? Enter like 0.05.
7. Chebyshev proving the law
With variance 4 and epsilon 0.1, the Chebyshev bound on P(average strays more than 0.1 from mu) is 4 over (n times 0.01). For n = 8000, compute the bound. Enter like 0.05.
8. Monte Carlo area
4000 uniform darts hit the quarter circle 3130 times. The area estimate is 3130/4000 = 0.7825. Four times that estimates pi. Enter the estimate rounded to two decimals, like 3.13.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.