统计与概率

Statistics & Probability

考点概述

离散/连续分布、条件概率、期望与方差

STEP 2/3 分开核验。复数与 2×2 矩阵可属 STEP 2；De Moivre、一般复根、平面与向量积等属 STEP 3。

学习重点

以下例题重点在于理解解题思路，建议先尝试自己解，再对照讲解。

1范围内书面例题

A bag contains $r$ red balls and $b$ blue balls, where $r,b \ge 1$ . Two balls are drawn at random without replacement.

Find the probability that both balls are the same colour.

Show that the probability that both are the same colour equals $\dfrac{r^2+b^2-r-b}{(r+b)(r+b-1)}$ .

Find, in terms of $r$ and $b$ , the expected number of red balls drawn.

Explain intuitively why $\mathbb{E}[X] = \dfrac{2r}{r+b}$ makes sense.

知识点已掌握？开始专项刷题！

题库根据此知识点精选，难度从基础到挑战逐步递进。