Chebyshevs inequality does not always give a better estimate

Chebyshev’s inequality does not always give a better estimate than Markov’s inequality. Let X be a random variable with E[X] = 2 and Var(X) = 9. Find the values of t where Markov’s inequality gives a better bound for

P(X > t) than Chebyshev’s inequality

Solution

P( x > t )

1 + 1/ k^2 = 9

k = 0.3535

T = 0.3535