{The Sphere [continued]}[22nd July 1988]

[Redbook5:219][19880722:2307b]{The Sphere [continued]}[22nd July 1988]

19880722.2307

[continued]

*This pattern of Binomial** Coefficients, which is of use in calculating probabilities, corresponds (in each line)* to the coefficient of the xy terms when (x+y)ⁿ is expanded for various values of n; for example: (x+y)⁵ = x⁵+5x⁴y+10x³y²+10x²y³+5xy⁴+y⁵.***

In Statistics, the Binomial Distribution is the most important discrete distribution.****

A Binomial experiment is is an experiment for which the following conditions are satisfied:

1. The experiment consists of a fixed number of trials (n)

2. Each trial has only 2 possible outcomes (usually called ‘success’ and ‘failure’)

3. The outcome of any trial is independent of the outcome of any other trial

4. The probability of success is constant from trial to trial.#

If the number of trials is sufficiently large, the Normal Distribution method can be used to approximate quite accurately the Binomial Distribution. The Normal Distribution #* is the most important continuous distribution in Statistics. 

 The significance of this – to my unmathematical mind – is in the possibility of a link with the uncertainty in Heisenberg’s principle if it really does exist other than as a limitation of our own measurement ability.

*[See last previous entry]

**(Binomial = An expression (e.g. equation) having 2 variables)

***(per Collins Gem Basic Facts Mathematics)

****It is also useful in Combinations and Permutations. <880724>

#Confusing[ly] called π! (Probability of failure = 1- π)

(per Hayslett, Statistics Made Simple)

#*[A small in-line image of a normal distribution curve is in the ms here, similar to the following but smaller and without figures or horizontal axis: ]

[continues]

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