This Work Including Others Where Posted To Prof. Sitsof E. Anku And GAAS In The Years 2010 And 2009

Hi Prof!

Good day. Find attach and appeal, models and theories presented to your outfit for necessary action.

Thanks.(said by me on Tuesday, February 9,2010).

ADONGO’S DIMENSIONAL THEORY OF RANDOMIZATION

INTRODUCTION:

Dimension is one of the world’s deepest mysteries.  No one can say exactly what it is.  Yet, the ability to measure dimension make our way of life possible.

Most human activities involve groups of people acting together in the same place at the same dimension.

One way of thinking about dimension is to imagine a world without dimension; dimensionless world would be at a standstill.  But if some kind of change took place, that dimensionless world would be different “now” than it was “before”.  The dimension – no matter how brief-between “before” and “now” indicates that dimension must have passed.  Thus, dimension and change are related because the passing of dimension depends on changes taking place.  In the real world changes never stop happening.  Some changes seen to happen only once like the falling of a particular leaf.  Other changes happen over and over again, like the breaking of waves on the shore.

Physically, I think of dimension as fundamental quantities that can be measured.  These fundamental quantities can be length, mass, population, or any entity.

The noted physicist Albert Einstein realized that measurements of these quantities are affected by relative motion.  Because of his work, time became popularly known as the fourth dimension.

Because of all these reasons about dimension, I have made an attempt to invent a theory called dimensional theory of randomization(or least whole normal theory) to enhance the contribution of knowledge to the nation development.

THEORY:

At greater than, γ % level of uncertainty for practical consideration of the random dimensional function D_x such that D_x(x) = αx – x^0.5 – β for all dimensions consist of all dimensional points (x, y) such that y = αx – x^0.5 – β. If y is a dimension which varies randomly due to change in the dimension x, then the dimensional equation in which y ≈ 0.00 and y ≈ + P_x provided all production dimensions are distributed normaly is given as:

2α.x^0.5 = 1 + (1 + 4αβ)^{0.5 ------------------------(1)}

For y ≈ 0.00

D_x (x) = α x – x^0.5 – ε ------------------------(2)

For y ≈ + P_x

Where α, β, and ε, are denoted as quintile coefficient of x, quintile constant at y ≈ 0, and quintile constant at y ≈ + P_x respectively.

Quantile coefficient and Quantile constants

At greater than γ % level of doubt for practical consideration of the random dimensional function D_x, the quantile coefficient, quantile constant at y ≈ 0 and quantile constant at y ≈ + P_x are given as;

                             

 α =  Θμ/[Ф^-1 (γ) (ΘS² + μ²σ²)^0.5]

                                                           

  β =  P_x/[Ф^-1 (γ) (ΘS² + μ²σ²)^0.5]    for y ≈ 0.00

 

EXAMPLE:

Each hour the television in Savanna hall JCR is switched on, the number of students who go in to watch the television has a distribution with mean 100 and variance 900.

The sachets of pure water purchased by each student had a Poisson distribution with mean 5.  The number of students going in to watch the television each hour it switch’s on and number of sachets  purchased by each student are independent.

(a)                Determine the least number of whole hours the television should be left on, so the uncertainty that 10,000 sachets of water will be purchased is greater than 95%.

(b)               If we expect to switch off the television every 12hrs; determine the sachets of pure water that are expected to be purchased in this given whole number of hours.

NOTE: Data given above is not a true data.

SOLUTION

(a) Mean of population demand (Θ) = 100

Variance of population demand (σ²) = 900

Production mean of a unit sample (X) = 5

Production variance of a unit sample (S²) = 5

Least whole overall production sample size (n_lw) = 10,000

The quantile coefficient and quantile constant are calculated as;

                  

                          

α =500 /[1.645 x 151.60]  = 2

 β =10,000 / 1.645 x 151.60= 40

The least number of whole hours is calculated as;

√ T_lw  =  [1 +  (1 + 320)^0.5] /4

 

√ T_lw  = 4.73

T_lw  = 22.4hrs (round up to 23hrs)

(b) n_lw = 1.645 (2(12) - √12) (500 + 22,500)^0.5

n_lw = 1.645 x 20.54 x 151.66

n_lw = 5,124.33 (round up to 5125)




REFERENCE
Adongo Ayine William(Me),Diary(2009), Posted(EMS) to Ghana Academy of Arts and Sciences in the Year, 2010.

INVENTED BY:

WILLIAM AYINE ADONGO