A Famous Mathematician Who Made a Significant Contribution to Statistics or Probability
Gauss, also known as the Prince of Mathematicians, contributed significantly to most areas of mathematics of the nineteenth century. He was a German mathematical genius who carried out much of the intellectual foundation for statistics, given his work in probability and statistics in particular. He may be mainly remembered for the least-squares method (handling measurement errors) (Bellos, 2020). As a committed perfectionist, he did not publish much of his studies, preferring to rework on theorems first and then improve them later. After his demise, his innovative exploration of non-Euclidean space has been found in his documents (Adeniran, 2020). During his astronomical statistical analysis, he noticed that a bell curve was created by sampling error-and that shape is now regarded as a Gaussian distribution.
Binomial Experiment
A Binomial Distribution is used to depict either (S) success or (F) failure. The binomial distribution formula is: b(x; n, P) = nCx × Px × (1 – P) n – x Where: b = binomial probability, x = total number of “successes” (pass or fail, heads or tails), P = probability of a success on an individual trial and n = number of trials.
Example
60% of youths who buy luxury vehicles are women. If 10 vehicle owners are randomly selected, find the probability that exactly 7 are women.
Step 1
‘n’ and ‘X’ are identified from the problem. 10 vehicle owners are randomly selected), and X is 7.
Step 2
The first part of the binomial formula, n! / (n – X)! X!, is figured out. Substituting the variables: 10! / ((10 – 7)! × 7!), which equals 120.
Step 3
The probability of success” and the probability of failure “q” are then calculated. p = 60%, or 0.6. Hence, the probability of failure is 1 – 0.6 = 0.4 (40%).
Step 4
pX is then worked out, which is 0.67 = 0.0279936
Step 5
q (0.4 – 7) is worked out.
= 0.4(10-7)
= 0.43
= 0.064
Step 6
The three solutions from steps 2, 4, and 5 are then multiplied together to give the binomial experiment.
120 × 0.0279936 × 0.064 = 0.215.
And 0.215 is the binomial experiment for the problem.
References
Adeniran, A. T., Faweya, O., Ogunlade, T. O., & Balogun, K. O. (2020). Derivation of Gaussian Probability Distribution: A New Approach. Applied Mathematics, 11(06), 436.
Bellos, A., 2020. The 10 Best Mathematicians. [Online] the Guardian. Available at: https://www.theguardian.com/culture/2010/apr/11/the-10-best-mathematicians [Accessed 20 June 2020].