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







Related Discussions:- Binomial distribution, Assignment Help, Ask Question on Binomial distribution, Get Answer, Expert's Help, Binomial distribution Discussions

Write discussion on Binomial distribution
Your posts are moderated
Related Questions
hazard and safety measures when using utm machine

kinds of machine tempering

What are the Types of interface An interface can be regarded as an aggregate of conditions, rules and conventions which describes the information exchange, between two communic

what effects do external factors have on engineering metals


Explain the Moment of resistance? Sol.: The two equal and unlike parallel forces, the lines of action of which are not same, form couple. The resultant compressive force ( P

Process units should have staggered access from at least two directions. The space between battery limits of adjoining units should be kept clear and open. Do not consider the clea


Q. Standard factory formed insulation on Flanges and Valves? All fittings are to be insulated with standard factory formed insulation. All joints shall be buttered and sealed.

What is the limition of kkleins constraction?