Introduction to Probability · 免费预览
随机变量的独立性与分布之间的联系
独立随机变量及其联合 PMF 可分解这一规则，此外还有二项分布与超几何分布之间的联系及其应用。
1. Independence of random variables
Independence of random variables
2. Sums of independent Binomials
Sums of independent Binomials
3. Bridges between Binomial and Hypergeometric
Bridges between Binomial and Hypergeometric
4. Testing independence from a joint table
A joint PMF has P(X = 1, Y = 2) = 0, while P(X = 1) = 0.4 and P(Y = 2) = 0.25. What follows?
5. Summing Binomials
X is Binomial(5, 0.4) and Y is Binomial(3, 0.4), independent. What is the distribution of X + Y?
6. Factorized joint
X and Y are independent with P(X = 1) = 0.3 and P(Y = 2) = 0.6. What is P(X = 1 and Y = 2)? Enter a decimal like 0.18.
7. Marginal from the joint
A joint PMF gives P(X = 2, Y = 1) = 0.15 and P(X = 2, Y = 2) = 0.10, and these are the only cells with X = 2. What is P(X = 2)? Enter a decimal.
8. When the Binomial approximation applies
A jar holds 1000 marbles, 400 red. You draw 5 without replacement and count reds. The Hypergeometric is exact, but a Binomial approximation with p = 0.4 is excellent here. Its parameter n is what integer? Enter the 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.