exponential and geometric distributions exponential distributionsunlike uniform distributionsoccur quite commonly they are often used to model inter-arrival timese of cars entering highway or requests for web page they are especially important because they have the memoryless property considerfor examplethe concentration of drug in the human body assume that at each time step each molecule has probability of being cleared ( of no longer being in the bodythe system is memoryless in the sense that at each time step the probability of molecule being cleared is independent of what happened at previous times at time the probability of an individual molecule still being in the body is at time the probability of that molecule still being in the body is at time the probability of that molecule still being in the body is ( ) more generallyat time the probability of an individual molecule having survived is ( ) suppose that at time there are molecules of the drug in generalat time tthe number of molecules will be multiplied by the probability that an individual module has survived to time the function implemented in figure plots the expected number of remaining molecules versus time def clear(npsteps)"""assumes steps positive intsp float nthe initial number of molecules pthe probability of molecule being cleared stepsthe length of the simulation""numremaining [nfor in range(steps)numremaining append( *(( - )** )pylab plot(numremainingpylab xlabel('time'pylab ylabel('molecules remaining'pylab title('clearance of drug'figure exponential clearance of molecules the call clear( produces the plot on the left