1. The problem statement, all variables and given/known data In the Drude model the probability of an electron having a collision in an infinitesimal time interval dt is given by dt/[tex]\tau[/tex]. (a) Show that an electron picked at random at a given moment will have no collisions during the next t seconds with probability e-t/[tex]\tau[/tex]. (b) Show that the probability that the time interval between two successive collisions of an electron falls in the range between t and t + dt is (dt/[tex]\tau[/tex])e(-t/[tex]\tau[/tex]) (c) Show as a consequence of a) that at any moment the mean time up to the next collision averaged over alll electrons is [tex]\tau[/tex]. (d) Show that as a consequence of b) that the mean time between successive collisions is [tex]\tau[/tex]. 2. Relevant equations Probability of a collision per unit time = t/[tex]\tau[/tex] Poisson Distribution of Random Variables, Poisson(k,[tex]\lambda[/tex])= ([tex]\lambda[/tex]ke-dt/[tex]\tau[/tex])/k! 3. The attempt at a solution So I proved part (a) by using the Poisson Distribution of RV's. Part (b) I tried to do the same thing as part (a), but for the time interval I used (t+dt)-t which gave me a lambda of dt/[tex]\tau[/tex]. Then I used k = 1 and went from there and it worked until the exponent where I got e-dt/[tex]\tau[/tex] rather than e-t/[tex]\tau[/tex]. Part (c) and (d) are where I get lost and have no clue of what to do.