Random experimen(1)
An experiment whose outcomes are not known in advance , or can not be predicted, and each of its outcomes has the same chance . (e.g. tossing a coin, throwing a die, measuring the noise voltage at the terminals of a resistor etc.)
Sample space
The sample space of a random experiment is a mathematical abstraction
used to represent all possible outcomes of the experiment, denoted by S .
Random event
An event on the sample space is represented by an appropriate collection
of sample point(s), that is a subset of a sample space, denoted by E.
For example, 1) considering the a random experiment of throwing a die, then
The sample space S or= ?={1,2,3,4,5,6}
The events are of number 2^n , n=6. Then {S,?,{1},{2},{3},{4},{5},{6},{1,2,3},{1,2,4},{1,2,5},{1,2,6},{4,5,6},{4,5,3},{4,5,2}
{4,5,1},{2,3,4},{2,3,5},{2,3,6},{1,3,4},{5,3,4},{6,3,4},{3,4,6}, {1,2,3,4},{1,2,3,5},{1,2,3,6},{5,2,3,4},{6,2,3,4},{3,4,5,6},{1,2,3,4,5},{2,3,4,5,6},
{1,2,3,4,6}}= is a set of all events of this sample space.
Event Space :is a set of all events, of number 2^n, of the sample space S.
2) Example 2 considering the a random experiment of tossing a fair coin
a) for only one time b) for two times. What is 1) the sample space ,
2) the event space for each case.
Sol. Case (a) Tossing a fair cion for only one time,
Then ?={H,T} , the event space =F={?,?,{H},{T} }