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

What is the spindle and drill, What is the spindle and drill The spindl...

What is the spindle and drill The spindle and drill head assembly the taper hole can be create on radial drilling machine with some special attachment likewise quill(The spindl

Determine fraction of the load would cnt fibers carry, Carbon nanotubes (CN...

Carbon nanotubes (CNTs) with low weight (density = 1.3 g/ cm^3), high tensile strength (50 GPa), and modulus of elasticity (1 TPa) in the axial direction have been touted as the st

What is heat treatment and why is it done, What is heat treatment and why i...

What is heat treatment and why is it done? Heat treatment can be described as a combination of operations or processes in which cooling and heating of an alloy or metal is done

How can you implement permeability test, Q. How can you implement Permeabil...

Q. How can you implement Permeability test  As already defined, permeability of porosity of the moulding sand is the message of its ability to permit air to flow through it.

Micrometer or screw gauge-measuring tools , Micrometer (or Screw Gauge): T...

Micrometer (or Screw Gauge): There are two different types of micrometers - inside and outside micrometers. A micrometer also has two scales - Main scale and Vernier scale (Figure

Evaluate the stresses in the concrete and steel bars, A load of 1.9 MN is a...

A load of 1.9 MN is applied on a short concrete column 300mm x 300mm. The column is reinforced with four steel bars of 10mm diameter, one in each corner. Evaluate the stresses in t

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

Find speed for two hours with hss tools, Find speed for two hours with HSS ...

Find speed for two hours with HSS tools Find speed for two hours tool life for dry machining of free cutting mild steel with HSS tool. Solution From Table 3, a value o

Platforms - planning of railway stations, Platforms: Platforms are pl...

Platforms: Platforms are places where trains stop and passengers entrain and detrain. For BG operations, the length of the platform should be about 30 m. Figure gives the

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