Introduction to Probability · 免费预览
次序统计量
样本排序后的取值（作为随机变量）、它们的边缘分布、均匀分布的间距，以及指数分布的最小值。
1. The k-th smallest as a random variable
The k-th smallest as a random variable
2. Uniform order statistics and spacings
Uniform order statistics and spacings
3. Extremes, minima and applications
Extremes, minima and applications
4. The maximum's CDF
Five independent variables share CDF F. What is the CDF of the maximum?
5. Minimum of Exponentials
Two independent components have failure rates 3 per year and 4 per year. The system fails when the FIRST fails. What is the failure rate of the system?
6. Median of three uniforms
The k-th smallest of n independent Uniform(0,1) draws is Beta(k, n+1-k). For the median of 3 draws, that is Beta(2, 2). What is its mean k/(n+1)? Enter a decimal like 0.5.
7. Rank density multiplier
For n = 4 samples, the density of the second smallest has multiplier 4 factorial over (1 factorial times 2 factorial). Compute it. Enter an integer.
8. Uniform spacing mean
Six uniform points cut the unit interval into 7 spacings. What is the mean length of any one spacing? Enter a fraction like 1/7.
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.