# chebychev's inequality

1. ### Different solutions when using direct calculation and Chebychev's inequality

Hi all, I have a question that I can't find answer to: I have 10 random variables X1, X2....X10 which are all independent and exponentially distributed with parameter=2 Xi~exp(2) for i between 1 and 10. Now the argument says that the probability that the sum of all 10 X's is larger...
2. ### Xn~Exponential(.5) -> Xn~Normal. Use Chebychev's inequality

Xn are iid Exponential(.5). After using the central limit theorem, Xn is Normally distributed. Use chebychev's inequality to find out how large n be so that P(|Xn-2| < .01) > .95. I tried working on it and got the E(Xn) = 2n and Var(Xn) = 4n, and P(|Xn-2n| > .01) < (4n/(.01)^2)(1/n)= 40000...