CHAPTER 2 A REVIEW OF BASIC STATISTICAL CONCEPTS
CHAPTER 2 A REVIEW OF BASIC STATISTICAL CONCEPTS
2.1 SOME NOTATION 1. The summation Notation 多x, 答、 can be abbreviated as:∑x,or∑x 2. Properties of the Summation Operator kX=k>x ∑(X1+Y)=∑X+∑Y ∑(a+bX1)=m+b∑X
2.1 SOME NOTATION • 1. The Summation Notation can be abbreviated as: or • 2. Properties of the Summation Operator = = = + + + i n i Xi X X X n 1 1 2 = − i n i Xi 1 Xi X X = = n i k nk 1 kXi = kXi Xi +Yi =Xi +Yi ( ) a + bXi = na + bXi ( )
2.2 EXPERIMENT SAMPLE SPACE SAMPLE POINT AND EVENTS 1.E× periment A statistical/ random experiment: a process leading to at least two possible outcomes with uncertainty as to which will occur 2. Sample space or population The population or sample space: the set of all possible outcomes of an experiment 3. Sample Point Sample point each member, or outcome, of the sample space(or population)
2.2 EXPERIMENT, SAMPLE SPACE, SAMPLE POINT, AND EVENTS 1. Experiment A statistical/random experiment: a process leading to at least two possible outcomes with uncertainty as to which will occur. 2.Sample space or population The population or sample space: the set of all possible outcomes of an experiment 3. Sample Point Sample Point : each member, or outcome, of the sample space (or population)
2.2 EXPERIMENT SAMPLE SPACE SAMPLE POINT AND EVENTS 4。E∨ents An event: a collection of the possible outcomes of an experiment; that is, it is a subset of the sample space Mutually exclusive events the occurrence of one event prevents the occurrence of another event at the same time Equally likely events: one event is as likely to occur as the other event Collectively exhaustive events: events that exhaust all possible outcomes of an experiment
2.2 EXPERIMENT, SAMPLE SPACE, SAMPLE POINT, AND EVENTS • 4. Events An event: a collection of the possible outcomes of an experiment; that is, it is a subset of the sample space. Mutually exclusive events: the occurrence of one event prevents the occurrence of another event at the same time. Equally likely events: one event is as likely to occur as the other event. Collectively exhaustive events: events that exhaust all possible outcomes of an experiment
2. 3 RANDOMVARIABLES o A random/stochastic variable(rv. for short):a variable whose (numerical) value is determined by the outcome of an experiment. (1)A discrete random variable --an rv. that takes on only a finite (or accountably infinite) number of values (2)A continuous random variable -=an rv that can take on any value in some interval of values
2.3 RANDOM VARIABLES • A random/stochastic variable（r.v., for short）: a variable whose (numerical) value is determined by the outcome of an experiment. • （1）A discrete random variable—— an r.v. that takes on only a finite (or accountably infinite) number of values. • （2）A continuous random variable——an r.v. that can take on any value in some interval of values