Please help with Question1 and Question 2b and c.

QUESTION 1 Let X1,X2,X3, . .. be i.i.d. Poisson (10) random variables, and for each it let Sn 2 X1 + X2 + - - - + X\". For large n, nd a value on so that P(|Sn 10n| > c\") z 0.1 QUESTION 2 In each part, provide calculations or reasoning. (a) For two random variables R1 and R2, E(R1) = 7, Var(R1) = 9, E(R2) = 8, Var(R2) = 25, and CO'U(R1,R2) = 10. Let R3 = 6R2 8R1 22. Find Var(R3). (b) Let X1 and X2 be i.i.d. with probability generating function G(s) = 0.2 + 0.255 + 0.154 + 0.155 + 0.15s7 + 0.2310, s 6 IR Find P(X2 > X1 + 6). (c) Let Y1,Y2,Yg,... be i.i.d. beta (3, 2) random variables. For large n, the random variable i211 Y? is very likely to be close to a numerical constant. What is the constant, and Why