<p>Meeting #1: Empirical distribution and histogram. 1) Let X be an attribute of a population with distribution according to Weibull distribution function with parameters lambda=1 and alfa=2,5. The following N=100 elements sample was taken:</p><p> a) Draw histogram in two ways: number of classes k equals integer of (1 + 3.322logN) and number of classes k= N b) Compare your results with theoretical distribution.</p><p>2) Electrical capacity of titanium plates was measured (in pF 103) and the following results were obtained: 11.0, 9.2, 9.9, 12.0, 8.0, 8.7, 7.1, 11.8, 11.7, 10.3 11.2, 8.1, 9.5, 11.5, 11.6, 9.7, 10.2, 11.4, 8.6, 10.0 a) Calculate sample mean and dispersion. b) Draw histogram</p><p>3) Svedberg observed tiny colloid of gold in microscope during constant period of time. Below the results are presented, where nj stands for number of periods in which j gold particles were observed.</p><p> a) Calculate sample mean and variation. b) Draw histogram n c) Compare empirical (sample) distribution pˆ = j with theoretical Poisson j n distribution with parameter lambda=1.54.</p><p>4) Observation from university book-shop shows the following expenditure of N=48 students (in zlotys)</p><p> a) Calculate sample mean and dispersion when sample elements are pre-grouped and when they are not grouped. b) Draw histogram c) Calculate median, mode, curtosis and excess. d) Discuss symmetry and “flatness” of sample distribution. 5) Life-time of electric lamps T (in hours) was investigated. The following N=200 observations are presented below: </p><p> a) Draw histogram b) Compare histogram with density function of exponential distribution with parameter lambda=0.00115. c) Compare theoretical and sample frequencies for every section of observations.</p>