Introduction to Probability · 免费预览
随机变量及其分布
把随机变量看作样本空间上的数值函数，把 PMF 看作完整的概率画像，把具名分布看作一个个故事。
1. Random variables
Random variables
2. The distribution and the PMF
The distribution and the PMF
3. Named distributions are stories
Named distributions are stories
4. Random variables are functions
Three coins are tossed and X is the number of heads. The statement X = 2 is shorthand for what?
5. Spotting the distribution story
A bakery sells 3 of its 12 remaining croissants to each of the first 4 customers, who each pick one at random, and you count how many of the 4 picked croissants were chocolate, given 5 of the 12 are chocolate. Which distribution does the count follow?
6. A PMF must sum to one
A random variable takes values 1, 2 and 3 with probabilities 0.5, 0.3 and c. What is c? Enter a decimal like 0.2.
7. Summing a PMF tail
For the number of heads X in three fair tosses, what is P(X is at least 2)? Enter a fraction like 1/2.
8. Bernoulli basics
A single biased coin shows heads with probability 0.35. For the Bernoulli random variable X that is 1 on heads and 0 on tails, what is P(X = 0)? Enter a decimal.
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.