Duplicate the steps used in the proof of Theorem 8 to prove Chebyshev's theorem for a discrete random variable X.
Theorem 8
(Chebyshev's Theorem) If μ and σ are the mean and the standard deviation of a random variable X, then for any positive constant k the probability is at least
that X will take on a value within k standard deviations of the mean; symbolically
![](https://test.transtutors.com/qimg/025ead58-3bdb-4397-b727-8a7fc3f96df0.png)