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Chebysef's Inequality Problem

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2. (Moments and Chebyshef's inequality, 8 points) A random variable X has E[X] = 10 and Var[X] = 100.
(a) Find the smallest upper bound for P(X (greater than or equal to) 40)
(b) Can X be a binomial random variable?
(c) Can X be a Poisson random variable?
(d) Can X be Exponential?

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This solution discusses a problem involving Chebysef's inequality.

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a) Var (X) = 100
Standard Deviation (X) = 100^0.5 =10
Now 40 is 3 standard deviation away from the mean. The smallest upper bound for P(X>=40) is determined by the Chebyshef's ...

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