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)?

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.

Demonstarte with your examples data.

Answer 1

Solution :

Suppose you toss two coins and the random variable is defined as getting a head. The possible outcomes are {TT,HT,TH,HH}. So, the number of Heads can be 0/1/2.Here, We are measuring the probability of occurrence of the defined Random Variable

Random Variable(Getting a Head)	Probabaility
0	1/4=.25
1	2/4=0.5
2	1/4=0.25

Here, the Sample Space is {TT,HT,TH,HH} and Sample Size is 4

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