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
(a) A circular cylinder of mass M and radius R connected by a spring of stiffness ‘K'. It is free to roll on horizontal surface without slipping. Calculate the natural frequency.

Air flows steadily at the rate of 0.5 kg/s through an air compressor, entering at 7m/s velocity, 100 kPa pressure, and 0.95 m 3 /kg volume, and leaving at 5 m/s, 700 kPa, and 0.19

Calculations for the force to move a block: T wo blocks A and B having weight 4KN and 2KN respectively are in equilibrium position as shown in the figure given below. Coeffi

Forced Air Cooling: A fan makes a difference between natural air cooling and forced air-cooling. The fan supplies the required air to carry away heat from the engine cylinder

Explain concept of Drill Power feed of the spindle is a common feature. Also coolant system is a ordinary feature of the radial drilling machine. Radial drilling machines ca

Compressive Stress: The stress induced in a body, when subjected to two equal and opposite pushes as shown in figure (a) as a result of which there is an decrease in length

(a) What is an ideal gas ? How does it differ from perfect gas ? Write the different laws of perfect gas. (b) The pressure in a car tyre was checked at 15 o C temp. and reading

Traveling at a speed of 16.0 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the roa

what is dry ness fraction?

Seawater is boiled in a 5 liter kettle to produce drinking water.  In class we solved the steady-state version of this problem.  Here you are asked to consider the transient period