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A discrete distribution for X is given by the following tabte! -6 -5 -2 1 0,01 -1 5 7. 10 11 13 14 15 16 P(X) 0.01 0.05 0.2 0.01 0.1 0.03 0.1 0.08 0.02 0.07 0.05 0.01 0.03 0.03 0.1 0.02 0.01 0.020 Build vectors In R (you can copy/paste for speed): omega- c-8, 6, 5,3,-2,-1.0,1,2,5,6,7,9,10,11,13.14,15,16,20 ) pe( 0.01,0.05,0.2,0.01,0.1.0.03,0.1,0.01,0.08,0.02,0.07,0.05,0.01,0.1,0.03,0.02,0.01,0.03,0.02,0.05) a. Use R to compute j E(X). b. Uhe R to compute Var(X)- P(z) (2-4) either by using "sum p (omega mu) 2 )" or Var(X)- E(X) - E(X. c. Check to see how close a sample estimation gets.

A discrete distribution for X is given by the following tabte! -6 -5 -2 1 0,01 -1 5 7. 10 11 13 14 15 16 P(X) 0.01 0.05 0.2 0.01 0.1 0.03 0.1 0.08 0.02 0.07 0.05 0.01 0.03 0.03 0.1 0.02 0.01 0.020 Build vectors In R (you can copy/paste for speed): omega- c-8, 6, 5,3,-2,-1.0,1,2,5,6,7,9,10,11,13.14,15,16,20 ) pe( 0.01,0.05,0.2,0.01,0.1.0.03,0.1,0.01,0.08,0.02,0.07,0.05,0.01,0.1,0.03,0.02,0.01,0.03,0.02,0.05) a. Use R to compute j E(X). b. Uhe R to compute Var(X)- P(z) (2-4) either by using "sum p (omega mu) 2 )" or Var(X)- E(X) - E(X. c. Check to see how close a sample estimation gets.

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 discrete distribution for X is given by the foliowing table: -6 -5 -3 -2 -1 1. 5 9. 7. 10 11 13 14 15 16 20 P(X) 0.01 0.05 0.2 0,01 0.1 0.03 0.1 0,01 0.08 0.02 0.07 0.05 0.01 0.1 0.03 0.02 0.01 0.03 0.02 0.05 Build vectors in R tyou can copy/paste for speed): omega - cl-8,6, 5,3,2,-1.0,1,2,5.6.7,9, 10,11,13.14,15, 16,20 ) p-c(0.01,0.05,0.2,0.01,0.1,0.03,0.1,0.01,0.08,0.02,0.07,0.05,0.01,0.1,0.03,0.02,0.01,0.03,0.02,0.05 ) a. Use R to compute j E(X). b. Uhe R to compute Var(X) =2 P(z) (2 - ) either by using "sum p (omega mu) 2 )" or Var(X) - E(X) - E(X)". c. Check to see how close a sample estimation gets. Take a sample of 100 from omega (and with probabilities from p). Then compute "mean(x)" and varx). Try this for a few different samples. Then do the same with samples of 16.000. which should you expect to give more accurate estimates lining up to the "true" values in a,b O The samples of size 100 provide more accurate estimates for EX) and Var (X) O The saimples of size 16.000 provide more accurate estimates for E(X) and Var(X) OSample size does not influence accuracy of estimation.
Transcribed Image Text:A discrete distribution for X is given by the foliowing table: -6 -5 -3 -2 -1 1. 5 9. 7. 10 11 13 14 15 16 20 P(X) 0.01 0.05 0.2 0,01 0.1 0.03 0.1 0,01 0.08 0.02 0.07 0.05 0.01 0.1 0.03 0.02 0.01 0.03 0.02 0.05 Build vectors in R tyou can copy/paste for speed): omega - cl-8,6, 5,3,2,-1.0,1,2,5.6.7,9, 10,11,13.14,15, 16,20 ) p-c(0.01,0.05,0.2,0.01,0.1,0.03,0.1,0.01,0.08,0.02,0.07,0.05,0.01,0.1,0.03,0.02,0.01,0.03,0.02,0.05 ) a. Use R to compute j E(X). b. Uhe R to compute Var(X) =2 P(z) (2 - ) either by using "sum p (omega mu) 2 )" or Var(X) - E(X) - E(X)". c. Check to see how close a sample estimation gets. Take a sample of 100 from omega (and with probabilities from p). Then compute "mean(x)" and varx). Try this for a few different samples. Then do the same with samples of 16.000. which should you expect to give more accurate estimates lining up to the "true" values in a,b O The samples of size 100 provide more accurate estimates for EX) and Var (X) O The saimples of size 16.000 provide more accurate estimates for E(X) and Var(X) OSample size does not influence accuracy of estimation.
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