KADD 2022 Laboratorium 2 EN

From Łukasz Graczykowski

Contents 1 Zadanie 2 Results

Zadanie

Let X be a random variable that has a probability distribution function f(x):

Please do:

• Draw the probability distribution function f(x) (0.5 pkt)
• Draw the cumulative distribution F(x). Cumulative distribution has to be drawn numerically and analytically. (1 pkt)
• Calculate the probability P(5 <= X <= 10) (0.5 pkt)
• Calculate the expected value E(X) and compare with the analytic result (1 pkt)
• Calculate the variance V(X) and compare with the analytic result(1 pkt)
• Calculate mode (0.5 pkt)
• Calculate quantiles: (0.5 pkt)
  • lower quartile
  • median
  • upper quartile

Results

Plots:

Output:

 P(5<X<10) z gestosci: 0.245723
 P(5<X<10) z dystrybuanty: 0.245723
 Srednia z funkcji TF1: 5.98798

 Srednia analitycznie: 6
 Wariancja z funkcji TF1: 35.3988
 Wariancja analitycznie: 36
 Moda: 0
 x0.25: 1.74
 x0.5: 4.16
 x0.75: 8.32