题目
Problem
The continuous random variable G has probability density function f(g) given by
f(g) = { (1/15)(g + 3), -1 < g ≤ 2
{ 3/20, 2 < g ≤ 4
{ 0, otherwise
(a) Sketch the graph of f(g)
(2)
(b) Find P(1 ≤ 2G ≤ 6 | G ≤ 2)
(4)
The continuous random variable H is such that E(H) = 12 and Var(H) = 2.4
(c) Find E(2H² + 3G + 3)
Show your working clearly.
(Solutions relying on calculator technology are not acceptable.)
(6)
(Total for Question 4 is 12 marks)
题目中文翻译
连续随机变量 G 的概率密度函数 f(g) 为
f(g) = { (1/15)(g + 3), -1 < g ≤ 2
{ 3/20, 2 < g ≤ 4
{ 0, otherwise
(a) 画出 f(g) 的图像
(b) 求 P(1 ≤ 2G ≤ 6 | G ≤ 2)
连续随机变量 H 满足 E(H) = 12 且 Var(H) = 2.4
(c) 求 E(2H² + 3G + 3)
清楚地展示你的计算过程。 （依赖计算器技术的解答不可接受。）
（第 4 题共 12 分）