solve this please

4. [Poisson Chances] Adhikari 7.4.1: Two radioactive substances emit o-particles indepen- dently of each other. The first emits X = Poisson(A,) particles. The second emits Y = Poisson(A,,). (a) Find the chance that X = 4 for A, = 2, then plot the p.m-f. for X. (b) Overlay the p.m.f. for Y if A, = 6. How does increasing the rate parameter A change the p.m.? (c) What is the probability that the first substance emits at least one a-particle? (d) Numerically, find the chance that both substances emit at least 3 particles. (e) A counter records a particles from both emitters. Let 4 = X+Y. Find the distribution of 4 as a function of A, and Ay, then find the chance that the counter records at least 3 emission events when A, = 3.87 and A, = 5.41