Exercise in class (1) Given the following number: 51,53,54,56,56,56,56,57,57,57,58,59,63,63,64,65,66, 67,69,69,70,72,72,72,73,76 (a)Plot a histogram of this data using six intervals. (b)Plot the cumulative distribution also. Interval N CN 51-55 3 3 12 56-60 9 12 10 61-65 4 6 66-70 5 21 4 71-75 4 2 2 02520151050 0 76-80 1 26 525762677277 525762677277 Shanghai Jiao Tong University 16
Shanghai Jiao Tong University 16 Exercise in class (1)
Discrete Distributions If the distribution is given and we know that measurement x,will occur with frequency f then Mean: Variance: N ∑ (-2 L= i- il N 02= N ∑6 1=1 Shanghai Jiao Tong University 17
Shanghai Jiao Tong University 17 Discrete Distributions
Distributions Notice the difference between the mean and variance of a given distribution and the estimates for the mean and a variance from a finite sample Universe Finite sample Mean: u x Variance: Shanghai Jiao Tong University 18
Shanghai Jiao Tong University 18 Distributions
Continuous Distributions Increase the number of measurements and the intervals.Plot frequency f=frequency of measurements nuus distbuticn Shanghai Jiao Tong University 19
Shanghai Jiao Tong University 19 Continuous Distributions
Continuous Distributions 00 If we normalize the distribution such that f(x)dx=1 1 2 Fraction of f(x)dx measurements or data between x and X2 Shanghai Jiao Tong University 20
Shanghai Jiao Tong University 20 Continuous Distributions