Introduction to Probability · 免费预览
中心极限定理、卡方分布与学生 t 分布
无论各组成成分如何，标准化和都收敛于正态分布；此外还有带连续性校正的正态近似，以及用于样本方差和小样本情形的卡方分布与 t 分布。
1. The theorem
The theorem
2. Using the CLT well
Using the CLT well
3. Chi-square and Student-t
Chi-square and Student-t
4. The CLT's hypothesis
What does the central limit theorem require of the summands?
5. Continuity correction direction
Approximating P(discrete sum is at least 60) with a Normal, which value should you standardize?
6. Standardizing a sum
One hundred independent measurements each have mean 5 and standard deviation 2. The total has mean 500. What is its standard deviation? Enter an integer.
7. A CLT probability
With the total approximately Normal(500, 20 squared), compute P(total over 540) using standardization: (540 minus 500)/20 = 2. Enter 1 minus Phi(2), about what? Round to three decimals like 0.023.
8. Chi-square mean
A chi-square with 12 degrees of freedom has mean equal to its degrees of freedom. Enter that integer.
9. t versus Normal critical value
For a 95 percent two-sided interval with 8 degrees of freedom, the t critical value is 2.306 while the Normal's is 1.96. The interval is WIDER with t. By how much does the critical value exceed 1.96? Round to two decimals like 0.35.
10. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.