1/ A -ray source is briefly pointed at a detector with a block of attenuating material in between. Over a time T, 15 photons are transmitted through the block. If the detector efficiency at this energy is 80%, plot the probability distribution for the number of detected photons D.

2/ Suppose the number of transmitted photons in time T is the Poisson random variable N with a mean of 15. Conduct a Monte Carlo computer simulation of the detection with 50 trials and plot the histogram for D. What is the sample mean of D? Repeat with 200 trials and 1000 trials.

What shape do the histograms have? What probability distribution does D follow?