Is my approach corrrect for the following:

Let Y1,Y2,Y3, ... be (not necessarily independent) exponential random variables,

such that Yn has parameter n = 2^n. Define a new random variable Z as follows:

Z = Yn

n=1

Allow yourself to use the linearity of expectation, E [Y1 +Y2] = E [Y1] + E [Y2], even

in this countably infinite case. Then use Markov's inequality to show that:

P (Z 10) 0.1

P (Z 10) E[X]/10

E[X^n]=n!/^n

E[X]=1/ = 1/2

E[X^2] = 2/^2=2/(2^2)^2=2/16=1/8

1/2 + 1/8 = 5/8

P (Z 10) E[X]/10 = 5/8/10=1/16 which is less than .1