题目
Problem
The random variable W has a continuous uniform distribution over the interval [–6, a] where a is a constant.
Given that Var(W) = 27
(a) show that a = 12
(2)
Given that P(W > b) = 3/5
(b) (i) find the value of b
(2)
(ii) find P(–12 < W < b/2)
(2)
A piece of wood AB has length 160 cm. The wood is cut at random into 2 pieces. Each of the pieces is then cut in half. The four pieces are used to form the sides of a rectangle.
(c) Calculate the probability that the area of the rectangle is greater than 975 cm²
(4)
(Total for Question 5 is 10 marks)
题目中文翻译
随机变量 W 在区间 [–6, a] 上服从连续均匀分布，其中 a 是常数。
已知 Var(W) = 27
(a) 证明 a = 12
已知 P(W > b) = 3/5
(b) (i) 求 b 的值
(ii) 求 P(–12 < W < b/2)
一块木板 AB 的长度为 160 厘米。将木板随机切成 2 块。然后将每块切成两半。这四块木板用来组成一个矩形的四条边。
(c) 计算该矩形面积大于 975 厘米² 的概率
（第 5 题共 10 分）