Random variables: coin toss example and outcomes

Random Variables

• Random variables help us to view the collected data as an outcome of a random experiment. Consider the simple experiment of tossing a coin. If a coin is tossed, then one can observe either “head” (H) or “tail” (T ). The occurrence of “head” or “tail” is random, and the exact outcome will only be known after the coin is tossed. We can toss the coin many times and
• obtain a sequence of outputs. For example, if a coin is tossed seven times, then one of the outcomes may be H, H, T, H, T, T, T . This outcome is the consequence of a random experiment, and it may be helpful if we can distill the sequence of outcomes in meaningful numbers. One option is to summarize them by a variable X, which takes the values x1 = 1 (denoting head) and x2 = 0 (denoting tail). We have learnt from Chap. 6 that this can be described in the framework of a random experiment where Ω = {ω1, ω2} with the events A1 = {ω1} = 1 = head and A2 = {ω2} = 0 = tail. The random variable X is