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

Value of the maximum shear stress , Value of the maximum shear stress: ...

Value of the maximum shear stress: Illustrates that for a given maximum shear stress the minimum diameter needed for a solid circular shaft to transmit P kW at N rpm may be ex

Choose a wire rope for a vertical mine hoist, Choose a wire rope for a vert...

Choose a wire rope for a vertical mine hoist to lift a load of 55 kN from a depth of 300 metres. A rope speed of 500 metres/min is to be attained in 10 seconds.

Optimal feeder geometry, PART A A new process plant for ore processing ...

PART A A new process plant for ore processing is currently being planned. The design is only in the first stage. However, three requirements have already been clearly stated:

Determine the relative error, a) Determine the relative error if 2/3 is app...

a) Determine the relative error if 2/3 is approximate to 0.667. b) √29 = 5.385 and √Π= 3.317 Correct to 4 significant figures. Determine the relative errors in their sum and dif

Oil seal found still leaking-stator plate oil seal complaint, After trial i...

After trial if oil seal found still leaking: Dismantle engine and check crank shaft for run out which should not be more than 0.10 mm.

Process of a pneumatic proportional controller, Explain the process of a Pn...

Explain the process of a Pneumatic Proportional Controller and get its transfer function. What modification is needed to make it function as a proportional plus derivative controll

Material engineering, State the four classes of engineering materials 3 (b)...

State the four classes of engineering materials 3 (b) Identify the class which each of the following materials belong to. Present your answer in table form Silicone, concrete, chro

Define principal process for electron beam machining, Define Principal Proc...

Define Principal Process for Electron Beam Machining A beam of electrons is emitted from the electron gun which is basically following three points. 1. A cathode whic

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