Binomial distribution, Mechanical Engineering

Assignment Help:

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.


Related Discussions:- Binomial distribution

Co-efficient of thermal conductivity, State required Features of Fourier La...

State required Features of Fourier Law. What are the factors on which co-efficient of thermal conductivity (K) depends upon ? Write the unit of K.

Define the project scope, Q. Define the project scope? The Design Basis...

Q. Define the project scope? The Design Basis Memorandum defines the project scope. This includes basic design concepts and the basis and philosophies upon which the project s

Vibration, A bump/impact test is a simple technique used to determine a str...

A bump/impact test is a simple technique used to determine a structure’s natural frequency. Sketch a typical time wave response curve of such a test, then label the impact point an

Fatigue loading on materials, what are the factors that affecting the fatig...

what are the factors that affecting the fatigue behaviour of materials?

Determine the moment of resistance of the beam, Determine the moment of res...

Determine the moment of resistance of the beam: A circular beam of diameter 100 mm is subjected to bending. The maximum bending stress is restricted to 50 N/mm 2 . Determine t

Determine the velocity, Question The three freight cars are rolling alo...

Question The three freight cars are rolling along the horizontal track with the velocities shown in the Figure. After the impacts occur the three cars become coupled together a

Maximum bending moment, Maximum Bending Moment: The SF changes sign at...

Maximum Bending Moment: The SF changes sign at A, among A and B and at B. Let a section XX at a distance x from the end C as illustrated in Figure SF at section XX, F x

Statics, what are the common application of statics in industry

what are the common application of statics in industry

Estimating time, estimating time of boring, turning,milling?

estimating time of boring, turning,milling?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd