Introduction to Probability · 免费预览
累积分布函数与随机变量的函数
CDF 作为任意随机变量的通用刻画：它的性质，以及随机变量的函数如何获得自身的分布。
1. The CDF and why it outranks the PMF
The CDF and why it outranks the PMF
2. Reading the staircase
Reading the staircase
3. Functions of a random variable
Functions of a random variable
4. CDF properties
Which of these functions cannot be a CDF?
5. Interval probability from the CDF
A CDF has F(2) = 0.45 and F(5) = 0.85. What is P(2 < X is at most 5)?
6. Decoding a jump
A discrete CDF has F(3) = 0.55 and left limit F(3^-) = 0.25. What is P(X = 3)? Enter a decimal like 0.3.
7. Two-to-one transform
X is a fair die roll and Y is 1 when X is at least 5 and 0 otherwise. What is P(Y = 1)? Enter a fraction like 1/3.
8. Squaring injectively
X takes values minus 2, minus 1, 0, 1, 2 each with probability 1/5. Let Y = X squared. What is P(Y = 4)? Enter a decimal like 0.4.
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.