题目
(i) The continuous random variable X is uniformly distributed over the interval [a, b]
Given that P(8 < X < 14) = 1/5 and E(X) = 11
(a) write down P(X > 14)
(b) find P(6X > a + b)
(ii) Susie makes a strip of pasta 45 cm long. She then cuts the strip of pasta, at a randomly chosen point, into two pieces. The random variable S is the length of the shortest piece of pasta.
(a) Write down the distribution of S
(b) Calculate the probability that the shortest piece of pasta is less than 12 cm long.
Susie makes 20 strips of pasta, all 45 cm long, and separately cuts each strip of pasta, at a randomly chosen point, into two pieces.
(c) Calculate the probability that exactly 6 of the pieces of pasta are less than 12 cm long.
(Total for Question 2 is 11 marks)
题目中文翻译
(i) 随机变量 在区间 上服从均匀分布。
已知 且 。
(a) 写下 。
(b) 求 。
(ii) Susie 做了一条 45 cm 长的意大利面条。她在一个随机位置把面条切成两段。随机变量 表示较短那一段的长度。
(a) 写下 的分布。
(b) 计算较短那一段少于 12 cm 的概率。
Susie 做了 20 条 45 cm 长的面条，并分别在随机位置切成两段。
(c) 计算恰好有 6 段面条长度少于 12 cm 的概率。
（第 2 题共 11 分）