Sample and estimation

### In the previous chapters – we analyzed distributions (random variables) of various types. – We had complete information about the random variable. – We could accurately calculate the expectation and standard deviation of the distribution. ### From this chapter and in the following chapters – there will be a lack of information about the distributions. – We will try to discover the missing information using samples. – The problem is that a distribution refers to the entire population, while a sample refers only to a part of the population and therefore cannot accurately reflect the behavior of the entire population. ### Example – Let’s assume that we have an unfair coin, so that if we toss it, the probability of getting “heads” is 0.55 while the probability of getting “tails” is 0.45.
– The probabilities reflect the distribution of an infinite number of shots (the entire population).
– If we had the option of tossing the coin an infinite number of times, then exactly 55% of the time we would get “heads” and exactly 45% of the time we would get “tails”.
– But if we look only at a sample, for example a sample of 100 shots, we might get a “tree” 60 times (which is not exactly 55% but only close to 55%). ### Conclusion – A sample reflects the population inaccurately, but we can still learn something about the population from it. – The larger the sample, the more accurately it reflects the population.