2,Let X be a Poisson (mean-5) and Let Ybe a Poisson (mean-4). Let Z-X+Y.Find P(X-312-6) Assume X and Y are independent. 1 like to see answers for P(A), (B), P(AB), and and hence P(A B). Here A Yo...
Let X be a Poisson (mean = 5) and Let Y be a Poisson (mean = 4). Let Z = X + Y. Find P( X = 3 | Z = 6). Assume X and Y are independent. Show answers for P(A), P(B), P(AB), and and hence P(A|B). Here A = [X = 3], B = [Z = 6]
7. Let x(t) be a Poisson process having rate 6 5. a) P(X(1)=2] b) P(X(2) = 31x(1)s 2] c) P(X(2) = 31x(4) = 5] d) EIX(1)] e) Var[X(1)] (1D 7. Let x(t) be a Poisson process having rate 6 5. a) P(X(1)=2] b) P(X(2) = 31x(1)s 2] c) P(X(2) = 31x(4) = 5] d) EIX(1)] e) Var[X(1)] (1D
and Y ~ Geometric - 4 Let X ~ Geometric We assume that the random variables X and Y are statistically independent. Answer the following questions: a (3 marks) For all x E 10,1,2,...^, show that 2+1 P(X>x) P(x (3 = Similarly, for all y [0,1,2,...^, show that Show your working only for one of the two identities that are pre- sented above. Hint: You may use the following identity without proving it. For any non-negative integer (, we have:...