Random variables are used to model situations in which the outcome, before the f
ID: 3049708 • Letter: R
Question
Random variables are used to model situations in which the outcome, before the fact, is uncertain. One component in the model is the sample space. The sample space is the list of all possible outcomes (or a range of possible values). For each value in the sample space, there is an associated probability. The probability can either be an estimate of something that exists in the real world or it could be an exact value that comes from an ideal distribution. Sometimes identifying the sample space helps to remind you exactly what it is that you are measuring.
Think of something that you might want to measure that is affected by random variation. Identify what you want to measure, then describe its (approximate) sample space. Give a rough description of the probabilities associated with those values (you can simply specify if they are all the same probability or if values in one range will be more likely than values in another range). What would you say to a person who says that he or she "knows" what the outcome of an individual observation will be (an outcome of something that has not happened yet that is subject to random error)? Please answer these questions in your own words, as if you were actually talking to another person.
When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable can serve as a model. There is no reason to run R code.
Explanation / Answer
Example of an event subject to random variation:
The outcome of rolling a fair six-sided die once, with the faces numbered 1,2,3,4,5 and 6.
The sample space is the set of all possible outcomes: {1,2,3,4,5,6}
P(1) = 1/6, P(2) = 1/6, P(3) = 1/6, P(4) = 1/6, P(5) = 1/6, P(6) = 1/6
If the person I am talking to says that he/she know the outcome of rolling a die, I would say "When you are saying you know the outcome, you are actually guessing or providing a best estimate. In reality, the die is fair and every outcome is equally likely. So there is no way you can "know" what the outcome would be in future. You can never never predict the outcome with 100% certainty, because the outcome is a random variable with the six possible outcomes having the 6 mentioned values."
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