Introduction
Criminal justice is a legal system that establishes the basic codes of conduct for citizens by deterring and controlling crime or sanctioning lawbreakers with criminal penalties and rehabilitation. The criminal justice system consists of the law enforcement, court system and the corrections departments that work together to uphold the rule of law within the society. The criminal justice process involves a procedure starting with criminal investigation, conviction, and correction of the convict.
To understand the criminal behavior and criminology, statistical concepts, probability, and hypothesis testing using the mean distribution are important. These concepts explain the behavior patterns of criminals and their likelihood of committing criminal activities. Besides, these concepts are applicable in courts to determine the credibility of the witnesses and the evidence provided.
Application of mathematical concepts in Criminal justice
The knowledge of statistical concepts like the mean and standard deviation is useful in criminal justice. The mean calculations help to understand the psychological behavior of criminals and compare this behavior with the other population. In a sample population, it has been established that intelligence is normally distribution with an average IQ of 100 and a standard deviation of 15.
A sample study to test the IQ levels of prisoners will provide the data to establish whether the criminals are in any way different from the other population. Assuming that the IQ level of the prisoners in the sample study is an average of 80, the knowledge of Z score formula and area under a normal curve will be useful in establishing the proposition that the prisoners are different from normal population.
The probability normal distribution curve is useful in hypotheses testing such as investigating whether the IQ of prisoners is different from that of other population (Walker, 1999, p. 248). In establishing the variations between the sample population (prisoners in this case) and the normal population, a normal curve is used. Although the sample may or may not be normal, it can nevertheless be representative of the population.
A large number of samples will create a sampling population that is representative of the population. The normal curve enables making inferences about the population based on sample data collected. In criminal justice system, the assessment of the evidence adduced by witnesses determines the innocence or the guilt of the accused. This is similar to data collected in statistical analysis and a large sample size in this case, many witnesses is important in arriving at the verdict.
In justice system, the accused is innocent until proven guilty. This is the null hypothesis that can be accepted or rejected based on the testimonies from the witnesses. If the jury makes in judgment then an innocent person is imprisoned. This in statistics is type I error, which involve the rejection of the null hypothesis.
The acceptance of the null hypothesis of innocence requires more evidence. Type II errors arise when the jury erroneously sets free a guilty person where the null hypothesis of innocence is wrongfully accepted. The lack of absolute proof of innocence leads to the rejection of the null hypothesis of innocence. Statistically, the alpha level of 5% is set as a standard for the rejection of the null hypothesis. The alpha level is the highest probability that random variability in data caused the investigated effect.
The application of statistics in justice system also involves the analysis and interpretation of the facts against the accused (Karim, & Nahoun, 2001, p. 56). The data collected from a crime scene is evaluated in order to reach at decision. In the justice system, the evidence can be in the form of eyewitnesses, fingerprints, fiber analysis, and DNA analysis among others.
The data collected must meet certain standards for it to be acceptable as evidence before the jury. The evidence collected is the sample data that is representative of the whole evidence. Errors in judgment are avoided by keen analysis of the data collected to prove that the accused is innocent or guilty (Michael, 2003, p.4).
Many of the decisions in the justice system are binary in nature and as such, no certain decision is possible. This calls for a careful examination of the probabilities in order to arrive at the conclusion. The law enforcement authority usually considers the probability of arrest and conviction of the accused.
Order of Operations
The process of criminal justice involves a series of steps beginning with investigations to punishment or rehabilitation of the accused. The order of operations involved in mathematical calculations is procedural and so is the functioning of the criminal justice system. Various rules and decision-making are core part of this order of operation in the criminal justice system.
The order of operations in the criminal justice system is procedural involving initial investigations to seek evidence for a particular criminal activity and support an arrest (Sennewald, & Tsukuyama, 2001, p.4). Investigations conducted by the police, involve inspection of a person or property to gather the evidence of an alleged crime. If the investigations associate a specific person to a particular crime, the person is arrested and detained, pending the hearing of the case in court.
The district attorney then goes through the evidence provided by the investigations to determine whether the arrested person has a case to answer. The prosecutors deliberate on the strength of the evidence and the magnitude of the crime before deciding to charge the accused person.
If the prosecutor decides to charge the accused person with criminal activities based on the evidence provided, the prosecutor issues an indictment or files a charging document.
The indictment involves the cases dealing with capital offenses as defined by the Federal Rules of Criminal Procedure. “The prosecutor can provide evidence for an indictment to a grand jury who will decide to raise charges against the defendant in a closed hearing” (Presser, 2001, p.9).
Alternatively, the prosecutor can file a charging document and a preliminary hearing in the presence of the defendant and his or her attorney held. According to Presser (2001), “the defendant and his/her attorney can dispute the charges against the defendant in this after indictment. , the defendant appears in court and enters a plea of guilty or not guilty followed by detention of the defendant prior to beginning of the trial but can be released on bail” (p.16).
Before the commencement of the trial, the defense attorney negotiates with the prosecutor for the defendant to plead guilty in exchange for leniency. The trial occurs before a judge in the presence of defense attorney and the prosecutor. If evidence suggests that the accused is guilty of the accused crime, the judge passes a sentence that can be a fine, probation or a jail term or a combination of both.
The defendant has an option to appeal the ruling in the court of Appeal through the defense attorney. If the appeal is successful, the prosecutor can decide to file the charges a fresh or drop them altogether. The correctional facilities serve to detain the charged person until the expiry of the jail term. However, pardon on exceptional behavior will lead to the release of the inmate before the expiry of the sentence.
The procedural criminal justice system has a major bearing on how the system functions. “The central goal why the order of operations should be procedural is to promote accurate, speedy, and efficient assessment of a crime followed by punishment” (Michael, 2003, p.45). Failure of a criminal system to stick to this procedural law will conflict the values of promptness and efficiency of the judicial court system.
Conclusion
The majority of the decisions in the criminal justice systems always involve two options. In courts, the proof of innocence or guilt of the accused is dependent on the assessment of the evidence provided by use of hypothesis testing and probability.
However, failure to meet the standards of rejecting the null hypothesis leads to errors in the judgment. Analysis of the evidence provides a basis for the rejection or approval of the claim of innocence. The criminal justice system is procedural to promote efficiency and accuracy in the judicial court system.
Therefore, probability and order of operations play critical role in criminal justice system. While probability seeks to address issues like mean and standard deviations and validation of hypotheses, order of operations seeks to ensure that procedures are followed to ensure only the guilty ones face judgment.
Reference List
Karim, V., & Nahoun, J. (2001). Applied Crime Analysis. Oxford: Butterworth – Heinemann.
Michael, S. (2003). Research: Criminal Investigations. New York: Word Press.
Presser, H. (2001). Detailed Analysis and Interpretation of Crime. West Virginia: West Virginia Associated Press.
Sennewald, C., & Tsukuyama, J. (2001). The process of Investigation. Oxford: Butterworth-Heinemann.
Walker, J. (1999). Statistics in Criminal Investigation: Analysis and Interpretation. Maryland: Aspern Publishers. Print.