## Markov's Inequality

Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant.

For a > 0:

Markov's inequality is used
to present another significant proportion entitled Chebyshev's
inequality.

Example:

For random variable X greater than with
a binomial
distribution with probability of success equal to 0.3 and
number of trials equal to 100, determine the upper bound regarding
probability of X
greater than or equal to 50 using Markov's inequality.

Solution:

Given the following
values for Binomial distribution:

p = Probability of success = 0.3

N = Number of trials = 100

For Binomial distribution:

E(X) = Np = (100)(0.3) = 30

Using Markov's inequality:

Pr(X ≥ 50) ≤ 30/50 or

Pr(X ≥ 50) ≤ 0.6

p = Probability of success = 0.3

N = Number of trials = 100

For Binomial distribution:

E(X) = Np = (100)(0.3) = 30

Using Markov's inequality:

Pr(X ≥ 50) ≤ 30/50 or

Pr(X ≥ 50) ≤ 0.6