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Let $X$ have a Poisson distribution with $\mu = 100$. Use Chebyshev's inequality to determine a lower bound for $\Bbb{P}(75 < X < 125)$.

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The mean of X is 100 and the standard deviation of X is 10.


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P(75<X<125)=P(|X-100|<2.5(10)) – Amr Nov 7 '12 at 11:09
Can you explain how? – user48495 Nov 7 '12 at 14:15
The variance is $10$? – Dilip Sarwate Nov 7 '12 at 15:26
Sorry, I meant the standard deviation. I will edit my ansewr. – Amr Nov 10 '12 at 12:14

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