STA261H1 Lecture Notes - Lecture 2: Central Limit Theorem, Independent And Identically Distributed Random Variables, Random Variable

• School: UTSG
• Department: Statistical Sciences
• Course: STA261H1
• Professor: Shahriar Shams

Document Summary

Suppose x1, x2, is an i. i. d. sequence of random variables each having nite mean and nite variance . Then according to the central limit theorem as n , i. e. sample mean. Let y be a linear combination of all the xi"s with i ) where i = 1, 2, n. Y = a1x1 + a2x2 + anxn + b = aixi + b n. Xi=1 where a1, a2, , an, b are constants. Xi=1 ai i + b , a2 i . Let, x1 n (10, 2) and x2 n (20, 3) and y = 0. 4x1 + 0. 6x2. Then y n ( , ) with mean=0. 4 10 + 0. 6 20 = 16 and variance = (0. 4)2. 2 + (0. 62) 3 = 1. 4. E e b t e a u n t e b t f a n t e i a m ch t t. 0 w h e r e i i z n.