Introduction to Probability · 免费预览
多项分布
具有多个结果的分类试验、多项分布的 PMF 及其边际与条件结构，以及类别合并。
1. Several categories at once
Several categories at once
2. Marginals by lumping
Marginals by lumping
3. Conditioning one count
Conditioning one count
4. The multinomial PMF
In 4 independent trials with category probabilities 0.5, 0.3, 0.2, what is P(counts are exactly 2, 1, 1)?
5. A multinomial marginal
X is Mult_3(20, 0.2, 0.5, 0.3). What is the distribution of X_2 alone?
6. Lumping categories
Trials fall in four categories with probabilities 0.1, 0.2, 0.3, 0.4. You lump the first two categories together. The lumped count over 15 trials is Binomial(15, p). What is p? Enter a decimal like 0.3.
7. A negative covariance
For Mult_k(n, p) with n = 40, p_1 = 0.25 and p_2 = 0.15, Cov(X_1, X_2) equals minus n p_1 p_2. Compute the value. Enter like -1.5.
8. Conditioning shrinks the experiment
Mult_3(12, 0.5, 0.3, 0.2) is conditioned on X_1 = 7. The remaining counts (X_2, X_3) form a Mult_2 with how many trials, and with what probability on category 2? Give n as an integer.
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.