What is the population and sample in the coin flip experiment? As a new learner of statistics I have some basic questions. In the experiment of coin flipping, if the coin is tossed for n times and it has been replicated over k trials that means the n-coin-flip has been repeated for k times, then what is considered to be the population and sample of our experiment?
Thanks
 A: The notion of a population does not really apply to coin tosses, or a lot of other random experiments. The population is a concrete way to introduce the difference between a sample from a distribution and the distribution itself in introductory statistics courses. Lots of people carry the term population over to discussions of distributions. We often speak of population moments, but we are referring to the moments of a distribution. There is no actual population.
The population is not the same as the sample space. The sample space is the set of possible outcomes. There is no implied relative frequency of occurrence. For a coin toss, the sample space is {Heads,Tails}. For a fair coin, both outcomes have equal probability. For an unfair coin, which has the same sample space, one of the two outcomes will be more likely.
A: Let's let your n=2, that is, we'll toss 2 coins. k is irrelevant to specifying the population, so we'll leave it aside for now.
The experiment of interest is tossing 2 coins. The population or sample space is the set of all the possible outcomes. An outcome is a complete specification of what could possibly happen when you conduct your experiment. So when you toss 2 coins, the population or sample space is the set of 4 possible outcomes {HH, HT, TH, TT}.
Now, let's repeat the experiment k=5 times. You might observe the following outcomes on these 5 flips of 2 coins: HH, HH, HT, TT, HT. This is your sample. Based on this sample of size 5 you can calculate the relative frequency with which each outcome occurred by dividing the frequency with which each outcome occurred by the total number of trials. As you increase k from 5 to 50, to 100, to 200, to 1000, to 100,000 and beyond you will notice that the relative frequencies of the 4 possible outcomes will approach more and more certain values. In the case of both coins being unbiased, you'll notice as you increase the number of trials that the relative frequencies will approach the theoretical probabilities of each of the 4 outcomes = (0.5)*(0.5)=0.25.
