题目
A bag contains a large number of coins. It only contains 20p and 50p coins. A random sample of 3 coins is taken from the bag.
(a) List all the possible combinations of 3 coins that might be taken.
Let X represent the mean value of the 3 coins taken.
Part of the sampling distribution of X is given below.
| X-bar | 20 | a | b | 50 |
|---|---|---|---|---|
| P(X-bar = X-bar) | 4913/8000 | c | d | 27/8000 |
(b) Write down the value of a and the value of b
The probability of taking a 20p coin at random from the bag is p
The probability of taking a 50p coin at random from the bag is q
(c) Find the value of p and the value of q
(d) Hence, find the value of c and the value of d
Let M represent the mode of the 3 coins taken at random from the bag.
(e) Find the sampling distribution of M
题目中文翻译
一个袋子里装有大量硬币，只包含 20p 和 50p 硬币。 从袋中随机抽取 3 枚硬币。
(a) 列出可能抽到的所有 3 枚硬币组合。
设 X 表示这 3 枚硬币的平均价值。
X 的抽样分布部分如下所示。
| X-bar | 20 | a | b | 50 |
|---|---|---|---|---|
| P(X-bar = X-bar) | 4913/8000 | c | d | 27/8000 |
(b) 写出 a 和 b 的值。
从袋中随机抽到一枚 20p 硬币的概率为 p。
从袋中随机抽到一枚 50p 硬币的概率为 q。
(c) 求 p 和 q 的值。
(d) 从而求 c 和 d 的值。
设 M 表示随机抽取的 3 枚硬币中出现的众数。
(e) 求 M 的抽样分布。