The following can be considered as a random variable
c)The sequence of head and tail we observe
The number of heads we got over 10 tosses is not considered to be a random variable as it is a measurable function that can be calculated from the probability set of the observations taken over the 10 tosses.
The index of the first time we have the head is also not considered to be a random variable as the probability of the number of tails observed before the generation of a heads is a measurable function from the probability measure space.
The sequence of Head and tail we observe can be considered as a random variable as the observations entirely depends on the specific experiment being conducted and may or may not form a repeatable sequence and would thus contain random variable in each probability set.
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