Suppose that a continuous random variable X has mean, and variance . By writing and using a

Suppose that a continuous random variable X has meanµ, and variance ϕ. By writing 

and using a lower bound for the integrand in the latter integral, prove that 

Show that the result also holds for discrete random variables. [This result is known as Cebysev's Inequality (the name is spelt in many other ways, including Chebyshev and Tchebycheff).]

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= f(x − µ)²p(x)dx > Suite- (x − µ)²p(x)dx - {x;\x-μ>c}