For Physics students. In Probability, the exponential probability distribution dP function is defined by Aet where dt is a positive constant. A particular application of this distribution is to the decay of radioactive nuclei. In that case, the probability that a particular nucleus will decay at some time T in the interval from t=0 to t=t is given by P(0 Tt) = [e dt. (a) Show that the p.d.f. dP dt = e=2t is well defined i.e. show that he dt = 1. (b) Evaluate P(0 T t) = e- dt. (c) The probability that a particular nucleus will decay { = within a time interval called the half-life is . Deduce that the half-life is given by In 2 . (d) Using your answer to (b) in the case where T < <