KADD 2022 Laboratorium 2 EN

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==Zadanie==

Let X be a random variable that has a probability distribution function f(x):
[[File:wzor_lab2.png]]

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:
[[File:lab2_3.png]]

Output:
  P(5<X<10) from the density: 0.245723
  P(5<X<10) from the cumulative distribution: 0.245723
  Mean from the function TF1: 5.98798

  Mean analytically: 6
  Variance from TF1: 35.3988
  Variance analytically: 36
  Mode: 0
  x0.25: 1.74
  x0.5: 4.16
  x0.75: 8.32