The probability of digit d occurring is Pr (d) =log base 10(1+(1/d)), where d=1,2,3,....9. Calculate Pr(d) for d=1,2,3,...9, check that the sum of all probabilities is one, and graph the probability mass function in excel. Also, show mathematically that summation of Pr(d)=1. You are showing that Beford's Law implies a proper probability mass function.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Solution :
Given : Pr (d) = ; d= 1,2,3,....,9
1. Pr(d) for d=1,2,3,....,9
Pr(1) = =
= 0.3010
Pr(2) = =
= 0.1760
Pr(3) = =
= 0.1249
Similarly putting d = 4,5,6,7,8,9 following probability mass function is obtained:
| d | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Pr(d) | 0.3010 | 0.1760 | 0.1249 | 0.0969 | 0.07918 | 0.06694 | 0.05799 | 0.05115 | 0.04575 |
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