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i.i.d. Suppose X1, ... , Xn " F with mean u and variance o². Let X, denote the sample mean. Suppose c, d are real numbers with c < d. When sample size n is large, 1

i.i.d. Suppose X1, ... , Xn " F with mean u and variance o². Let X, denote the sample mean. Suppose c, d are real numbers with c < d. When sample size n is large, 1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(a) Suppose X1, ..., Xn i.i.d. ~ F with mean µ and variance o². Let X, denote the sample mean. Suppose c, d are real numbers with c < d. When sample size n is large, 1 use the Central Limit Theorem to approximate P (c < X, < d) . Please use the CDF of N(0, 1) in your approximation, which is denoted by P(x) in this course. As a reminder, (x) := S (27)-1/2 exp(-ť²/2) dt. Note: It's possible/OK to use the result here to solve some of the following questions where applicable (well, you will need to make sure your result here is correct). Or, if you prefer, you can work out the following questions without referring to this general result, as a practice to enhance your understanding of CLT.
Transcribed Image Text:(a) Suppose X1, ..., Xn i.i.d. ~ F with mean µ and variance o². Let X, denote the sample mean. Suppose c, d are real numbers with c < d. When sample size n is large, 1 use the Central Limit Theorem to approximate P (c < X, < d) . Please use the CDF of N(0, 1) in your approximation, which is denoted by P(x) in this course. As a reminder, (x) := S (27)-1/2 exp(-ť²/2) dt. Note: It's possible/OK to use the result here to solve some of the following questions where applicable (well, you will need to make sure your result here is correct). Or, if you prefer, you can work out the following questions without referring to this general result, as a practice to enhance your understanding of CLT.
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