Review of statistics Random errors in measurements are expressed with probability density functions that give the probability of values falling between x and xtdx Integrating the probability density function gives the probability of value falling within a finite interval Given a large enough sample of the random variable, the density function can be deduced from a histogram of residuals 03/1203 12540Lec10 xample of random variables ×x文x 0.00 800007 03/12/03 12.540 Lec 10 13 Review of statistics • Random errors in measurements are expressed with probability density functions that give the probability of values falling between x and x+dx. • Integrating the probability density function gives the probability of value falling within a finite interval • Given a large enough sample of the random variable, the density function can be deduced from a histogram of residuals. 03/12/03 12.540 Lec 10 14 Example of random variables -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.00 200.00 400.00 600.00 800.00 Uniform Gaussian Random variable Sample