Introduction to Probability · 免费预览
矩、偏度与样本矩
用原始矩和中心矩依次刻画分布形状，用标准化三阶矩和四阶矩表示偏度与峰度，用样本矩作为基于数据的估计。
1. Moments of all orders
Moments of all orders
2. Skewness and kurtosis
Skewness and kurtosis
3. Sample moments
Sample moments
4. Skewness direction
Household income distributions typically have skewness around +1.5. What does the positive sign indicate?
5. The n minus 1 divisor
Why does the sample variance divide by n minus 1 instead of n?
6. A raw moment by LOTUS
A fair die roll has E(X) = 3.5 and E(X squared) = 91/6. What is E(X cubed)? The sum of cubes from 1 to 6 is 441, so enter the value as a fraction in lowest terms and report the numerator.
7. Exponential higher moment
For Exponential with rate 1, E(T squared) = 2. Using the recursion E of T to the r equals r times E of T to the r minus 1, what is E(T cubed)? Enter an integer.
8. Method of moments for a mean
Exponential data has sample mean 0.4. The method of moments estimate of the rate lambda is 1/0.4. Enter that decimal, like 2.5.
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.