The government of Ghana has decided to automate the analysis of judged cases to flag out poorly judged cases and to determine whether the cases processed at the law court were fairly attended to or not. At artificial intelligent software using Bayesian filter is to be used to measure the intelligence in processing legal cases to determine whether a judgement made by judges are fair or not. A set of cases were fed into the memory of the software for processing the cases and determine fairness in the cases. The filter is to determine following probabilities: P(J)= probability that there was a judgement on the case and the judgement was fair. P(J’) probability that there was a judgement on the case and the judgement was not fair. P(E) Probability that there were evidences and the evidences were valid. P(E’) Probability that there were evidences and the evidences were not valid. Let P(J) = 0.85 be probability that there was a judgement on the case and the judgement was fair. Let P(E/J) = 0.13 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were fair. Let P(E/J’) = 0.82 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were not fair. Assuming you are part of the research team that induces the intelligence into the machine, solve the following questions below. Draw the Bayesian Network diagram in the form of tree diagram to form the basis of reasoning for the machine for the above situation. Calculate the probability that there was a judgement on the case and the judgement was not fair. P(J’). What is the probability of non-valid evidences based on the condition that there were judgements on the case and the judgement were not fair P (E’/J’)? What is the probability of non-valid evidences based on the condition that there were judgements on the case and the judgement were fair P (E’/J)?
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.
The government of Ghana has decided to automate the analysis of judged cases to flag out poorly judged cases and to determine whether the cases processed at the law court were fairly attended to or not. At artificial intelligent software using Bayesian filter is to be used to measure the intelligence in processing legal cases to determine whether a judgement made by judges are fair or not. A set of cases were fed into the memory of the software for processing the cases and determine fairness in the cases. The filter is to determine following probabilities:
P(J)=
P(J’) probability that there was a judgement on the case and the judgement was not fair.
P(E) Probability that there were evidences and the evidences were valid.
P(E’) Probability that there were evidences and the evidences were not valid.
Let P(J) = 0.85 be probability that there was a judgement on the case and the judgement was fair.
Let P(E/J) = 0.13 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were fair.
Let P(E/J’) = 0.82 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were not fair.
Assuming you are part of the research team that induces the intelligence into the machine, solve the following questions below.
- Draw the Bayesian Network diagram in the form of tree diagram to form the basis of reasoning for the machine for the above situation.
- Calculate the probability that there was a judgement on the case and the judgement was not fair. P(J’).
- What is the probability of non-valid evidences based on the condition that there were judgements on the case and the judgement were not fair P (E’/J’)?
- What is the probability of non-valid evidences based on the condition that there were judgements on the case and the judgement were fair P (E’/J)?
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