Meeting I: Empirical Distribution and Histogram

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:

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.

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

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.

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.

4) Observation from university book-shop shows the following expenditure of N=48 students (in zlotys)

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:

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.