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# Statistics 2037 - Chapter 16 Understanding Probability and Long Term Expectations.docx

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Department
Statistical Sciences
Course
Statistical Sciences 2037A/B
Professor
Semester
Fall

Description
Chapter 16 – Understanding Probability and Long Term Expectations Probability can be the estimation of our chances or personal beliefs. Relative frequency interpretation is the probability that applies to situations where we can see the results occurring over and over again. Probability is the relative frequency over the long run or the proportion of times it occurs over the long run. Wouldn’t use a family with one boy and four girls and say a 1/5 chance of getting a boy. We would use 1000 births and see the probability of having a boy as the relative frequency. To determine the probability of an outcome for relative frequency we can make an assumption about the physical world. Things that give every possibility an equal chance can be assumed. Example: flipping a coin, lottery chances. Does not necessarily mean it will happen exactly that many times per number of tests. We can also observe the relative frequency through many repetitions of a situation. Sometimes these are based on results from sample surveys. Relative frequency can be applied to probability when a situation can be repeated and an outcome can be observed. The relative frequency should become a constant value over the long run. This value is the probability. It does not apply when the outcome is affected by something one time and another the next time. Probability does not determine the outcome of a single occasion, just the long run. Relative frequency is very useful for daily decisions. Relative probability is limited to repeatable situations under the same conditions. Personal probability is the interpretation of situations that may never happen again. Example: better mark in calculus or stats, finding a parking spot. We assign personal probability to these situations based on our own knowledge and experiences. Different people may not agree on the probabilities of different outcomes. Personal probability is the degree to which an individual believes an event will happen. The probability must be between 0 and 1 (0% and 100%). It must also be coherent, it doesn’t contradict the probability of another event. We base a lot of decisions on personal probability. Example: committee decides what candidates are appropriate for the job, jury
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