From Łukasz Graczykowski
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) 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
