Probabilistic sample(or random sample, sample): One realizable phenomenon from the probabilistic problem you want to solve Or one sampled case Sample space $$$\Omega$$$: Set which contains all possible samples Task of defining sample sapce: Define which phenomenon is possible to occur and which phenomenon is impossible to occur ================================================== Sample space when you toss the coin $$$\Omega =\{H,T\}$$$ ================================================== Some cases has set of entire real numbers as sample space $$$\Omega = \mathbf{R}$$$ ================================================== Possible events: possible sub sets of sample space $$$\Omega$$$ Sample space $$$\Omega=\{H,T\}$$$ Possible events: $$$\phi,\{H\},\{T\},\{H,T\}$$$ ================================================== Probability is function which takes all events and which outputs number $$$P(A)=0.1$$$ P() is function P A is event 0.1 is probability value ================================================== Kolmogorov's axioms 1. $$$P(\text{all\_events})\ge 0$$$ 2. $$$P(\Omega)=1$$$ 3. If $$$A\cap B=\phi$$$, then $$$P(A\cup B)=P(A)+P(B)$$$ ================================================== Interpretion about probability value: 1. Frequentist 2. Baysian ==================================================