Question

Problem 4: Let X be a continuous variable with mean inequality find A 0 so that and variance ơ2. Using Chebyshev

Answer 1

The Chebyshev Inequality is as follows.

If X be a random variable such that var(X) exists and is positive, and if E(X)= $\mu$ and var(X)= $\sigma ^{2}$ , then

$P[|X-\mu | \geq t\sigma ]\leq \frac{1}{t^{2}}$

for any t>0.

There is also One sided Chebyshev Inequality. Which is

$P[X\geq \mu + t\sigma ]\leq \frac{1}{1+t^{2}}$

for any t>0