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

Staff holon, Figure: Structure and Relationship among the Basic Holons of...

Figure: Structure and Relationship among the Basic Holons of a Holonic Manufacturing System   Staff Holon The function of staff holon is to support other holons along

Different relations used in belt drive, Q. W rite different relations used...

Q. W rite different relations used in belt drive. Sol: Let: D 1 = Diameter of driver N 1 = Speed of the driver in Rotation per minute D 2 = Diameter of the driv

Define properties of system, Define Properties of System For defining a...

Define Properties of System For defining any type of system particular parameters are required. Properties are those observable characteristics of the system, which can be util

Describe soldering, Soldering Soldering is defined as a metal joining...

Soldering Soldering is defined as a metal joining process wherein coalescence is produced by heating the surfaces to be joined to a suitable temperature and melting the fille

Governor, sensitivity of governors

sensitivity of governors

Turnouts, Turnouts: A turnout is an assembly of various components wh...

Turnouts: A turnout is an assembly of various components whereby a train running on one track may be diverted to another. A sketch of a left-hand turnout is given in Figur

Total decrease in length - hollow cast iron cylinder, Total decrease in len...

Total decrease in length: Q: A hollow cast iron cylinder 4 m long, 300 mm is the outer diameter, and thickness of metal 50 mm is subjected to central load on top when standin

Simply supported beam - shear force diagram, Simply supported beam - Shear ...

Simply supported beam - Shear Force diagram: A simply supported beam of length 8 m is subjected to a consistently varying load from zero at centre to 3 t/m at both of ends. Dr

Estimate the machining time, Estimate the Machining Time A hollow work...

Estimate the Machining Time A hollow workpiece of 60 mm outside diameter and 150 mm length is held on a mandrel among centers and turned all over in 4 passes. If the approach

Piping, difference between pipe and tube

difference between pipe and tube

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