Chebychev probability

1. Apr 21, 2013

ParisSpart

A non-negative random value X such that

E[e^X]=19
If p be the probability that the random value is at least 5 then what is the least upper bound you can give for the probability p with this information?

i think that i must use the type of chebychev like this

p(X>=5)<=(E(X)/5) but we have E(e^X) if i put e^X=Y then i will have this

p(e^X>=5)<=(E(Y)/5) and i am taking ln(log) and i have: p(X>=5)<=19/5 but the quiz says that 19/5 its not correct any ideas?

2. Apr 21, 2013

fzero

If $X\geq 5$, what bound can you put on $e^X$?