Consider the map of the interval $x_{n+1}=4\mu x_{n}(1-x_{n})$, where $\mu\in[0,1]$. Using a Monte-Carlo technique, calculate the probability of finding a chaotic dynamicsin the parameter interval $\mu\in[\mu_{\infty}=0.892486,1]$.
The sugestion seems to be randomly select parameters in the interval $[0.892486,1]$, and calculate the respective Lyapunov exponents. How to I calculate the probability? I'm used to Python and Mathematica, if that helps.