Suppose that X1, X2, X3 and X; are independent Poisson where E[X1] : ACE-b E[X2] = A(1 (1)!) E[X3] = Aa b) E[X4] = A(1 a)(1 b) where a = 0.25, b = 0.5 and A = 2. Let S = X1+X2+X3+X4, R = X1+X2 and C = X1 + X3. (3.) Find 1P(R = 10) (b) Find 1P(X1 = 6 I 5' =16 and R =12). ((3) Suppose we want to condition on the event {5' = 1-4, R = 12, C = 10}, What are the possible values that X1 can take? (d) Find MA] = 10 | S = 14.1% =12,C =10)