22 Jul 2022

55

Probability, Random Variable and Sampling Distribution

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Academic level: College

Paper type: Essay (Any Type)

Words: 611

Pages: 2

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Probability refers to the likelihood that a certain event will occur. For example, in a football match, three events are likely to occur, that is, a team either wins, losses or draws. Another example to explain this includes the act of tossing a coin whereby the two probabilities are that the tail or head may face up. 

Conditional Probability refers to the type of probability in which the occurrence of one event depends on another. For example, in any tournament, the probability of a team to lift a trophy depends on its chance of participating in the event. In other words, the team cannot have a chance of winning the tournament, say the Olympic, without being a participant. 

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False Negative is a situation whereby when a test is carried out, it indicates negative but in a perfect condition, it is supposed to be positive. For instance, one may have negative results for diabetes due to errors but in reality, the person is suffering from diabetes. The condition can also be illustrated when a pregnancy test is carried out. One may be discovered not to be expectant but the actual results should indicate the other way round. 

False Positive refers to a situation whereby due to certain errors, a test indicates the presence of the variables being investigated but in reality, they are not available. For instance, an athlete may be found to be positive when a doping test is carried out. However, the athlete may be very innocent. 

Random Variable refers to a collection of values likely to be obtained whenever a random test is carried out such as the number of students that are absent on any day. 

Normal Curve or Normal Distribution is a theoretical curve illustrating how variables are likely to behave in any statistical test, and includes the number of students who pass or fail a test. The highest point usually occurs at the middle where a majority of the variables lie as illustrated below. 

Positive Skew occurs in distribution curves when longer tail falls on the positive peak’s side and it includes the income level of people. The sketch for a positive skew is indicated below. 

Negative Skew occurs in a distribution curve whenever the longer part of the tail falls in the negative side in the number line and includes household income. An example is indicated below. 

Standard Deviations in a Bell Curve is the two points between the negative and positive side, and a good example is in a class whereby the highest number of students are likely to perform averagely. 

Bernoulli distribution is a type of event whereby two chances are likely to occur, that is, a success or failure .Usually, a “Yes” is denoted by 1 while a “NO” is represented by a 0. A good example is when one is called over the phone since they can either decide to pick the call or reject it. Another example is when one is at the ATM. In this case, the user may be prompted to either reply with a yes or no in order to proceed with a transaction or to stop it immediately. 

Sampling Distribution is statistical distribution for the possible samples in any sample size of the population and includes the statistics for the presidential elections. 

Margin of Error is the range in which errors may be allowed to occur, and a good example may occur in carpentry whereby a carpenter may be right by allowing an error of plus or minus 3 centimeters. The condition occurs since some errors cannot be avoided such as the parallax error while taking measurement using different measuring instruments such as the meter rule. 

0.05 Threshold implies that a 5 percent chance occurs for an individual to obtain the desired results. For instance, when a sample involves 100 people, the result may be used with 95 or 105 respondents. 

Statistical Significance indicates the extent to which tolerance to risk and applicability has been achieved and it includes clinical significance as far as its application is concerned. 

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StudyBounty. (2023, September 16). Probability, Random Variable and Sampling Distribution.
https://studybounty.com/probability-random-variable-and-sampling-distribution-essay

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