题目
Problem
A bag contains a large number of balls, each with one of the numbers 1, 2 or 5 written on it in the ratio 2 : 3 : 4 respectively.
A random sample of 3 balls is taken from the bag.
The random variable B represents the range of the numbers written on the balls in the sample.
(i) Find P(B = 4)
(ii) Find the sampling distribution of B.
(10)
(Total for Question 4 is 10 marks)
题目中文翻译
一个袋子里有很多球，每个球上写着 1、2 或 5 之一，比例分别为 2 : 3 : 4。
从袋中随机抽取 3 个球。
随机变量 表示样本中所写数字的极差。
(i) 求 。
(ii) 求 的抽样分布。
（第 4 题共 10 分）