================================================================================ "Statistical phenomena" - Suppose there are undefined phenomena - You iteratively observe phenomena - You may find intrinsic pattern from those phenomena - In this situation, "those phenomena" is called statistical phenomena ================================================================================ - On statistical phenomena, you can perform "random experimental (or trial)" - Trial is what you can "iterate" under "same condition" - You can't predict results of every trials but you can know the set of all possible result For example, you don't know what number occurs in rolling the dice. But you know there are six possible events. - Each result will show in irregular pattern. But as you increase number of trials, results will show some pattern. ================================================================================ Through trial, you get "probability" - Probability is a metric which shows intensity of clearness on statistical phenomena. - Probability is the number which is assigned into events Example - Toss coin as trials - You can assign "probability value number" into events H and T ================================================================================ Sample space S: entire set which contains all possible events. ================================================================================ Mathematical probability - Suppose all events from sample space S have same probability of occuring, then, $$$\dfrac{n(A)}{n(S)}$$$ is mathematical probability of event A. $$$n(A)$$$: number of samples which are involved in event A $$$n(S)$$$: number of samples which are involved in sample space S ================================================================================ Example: a dice has 6 events ================================================================================ Statistical probability - Natural phenomena and social phenomena generally don't have phenomena which have same probability in each event. - In that case, how can you obtain probability? - It can be done also by performing trials. Example: - Toss coin many times - Probability on H is predicted by relative frequency - Relative frequency: suppose n trials and suppose event what you want to know happens r times then, you can write $$$\frac{r}{n}$$$ $$$\frac{r}{n}$$$ is relative frequency (r is not entire sample space)