Exercise: Chebyshev versus Markov

2 points possible (graded)
Let X be a random variable with zero mean and finite variance. The Markov inequality applied to [X] yields

P(IXI>=a)<=E[IXI]/a
whereas the Chebyshev inequality yields
P(IXI>=a)<=E[IX²I]/a²

a) Is it true that the Chebyshev inequality is stronger (i.e., the upper bound is smaller) than the Markov inequality, when is very large?

Select an option
unanswered
b) Is it true that the Chebyshev inequality is always stronger (i.e., the upper bound is smaller) than the Markov inequality?

1 answer

a) Yes
b) No