Binomial distribution, Mechanical Engineering

Binomial distribution:

Let X follow a binomial distribution with parameters n = 4 and p = 0.5. Tabulate P ( ¦X - μ¦ ≥ k ) and σ2/k2 for k = 1,2,3,4,5 and verify that Chebyshev's lemma is true for each k. Comment on the usefulness of σ2 /k2 as an approximation of  P ( ¦ X - μ ¦ ≥ k ).

Solution:

We have

Μ = np = 2, σ2  =npq = 1 and p(X =x) = 1314_Binomial distribution.png(.5)4 1314_Binomial distribution.png/16,

X= 0,1,2,3,4.

Therefore we obtain, in a tabular form

397_Binomial distribution1.png

Chebyshev's lemma is clearly satisfied for every k. However, the upper bound to the probability is weak and the estimate σ2/k2 - is not a good approximation to the probability.

Posted Date: 1/31/2013 5:24:09 AM | Location : United States







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