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
Q. Layout of vessels in plant design? Layout of vessels needs to allow sufficient spacing for instruments, piping, operations, maintenance and firefighting access. Vessels o

when the governor is connected to a engine its sensitiveness formula change,why?

Q. Corrosive properties of caustic? Sodium hydroxide, more commonly known as Caustic Soda or simply ‘Caustic', is widely used in the petrochemical industry to neutralize acidic

The Center Mark Command We can use  Center Mark command to annotate a circle or an arc with a cross at the center.Illustration above shows a center mark added to a circle quick

two different method to convert from rotational motion to liniar motion

Crankshaft : It converts the reciprocating motion of the piston into useful rotary motion. In the crankshaft of a single cylinder engine, there is a pair of crank arms and balance

A steam boiler, 3 m in diameter, is made of 25 mm thick mild steel plates. The efficiency of longitudinal riveted joint is 88% and that of circumferential riveted joint is 70%. Cal

Vibration Damping : Suitable mechanism should be incorporated within the clutch to eliminate (to reduce it drastically) noise produced in the transmission. Size : The size of

Average force of resistance: A gun weighing 500 kN is utilized to fire a shell weighing 10 kN in a horizontal direction with a velocity of 500 metres/sec. With what initial ve

Construct a retrograde Vernier scale: During construct a retrograde Vernier to a scale of 1/5, signify inches and 10 th , and 30 inches and long sufficient to read to mark dis