Mathematics Probability and Statistics
Mathematics Probability and Statistics
4.1 Random variables 。Definition the real-valued functions defined on the sample space -2 -1 0 3
4.1 Random variables • Definition the real-valued functions defined on the sample space -3 -2 -1 0 1 2 3
Random variables can be: Discrete random variables have a countable number of outcomes Examples:Dead/alive,treatment/placebo,dice,counts, etc. Continuous random variables have an infinite continuum of possible values. Examples:blood pressure,weight,the speed of a car,the real numbers from 1 to 6
Random variables can be: • Discrete random variables have a countable number of outcomes – Examples: Dead/alive, treatment/placebo, dice, counts, etc. • Continuous random variables have an infinite continuum of possible values. – Examples: blood pressure, weight, the speed of a car, the real numbers from 1 to 6
Example 1a roll of a die Probability mass function (p.m.f.) X p(x) 1 pX=1=1/6 p(x) 2 PX=2上=1/16 3 pX=31/6 1/6 4 P(X=4)116 1 ll 123456 5 pX=5上1/6 6 pX=6F1/6 ∑P(x)=1 all x
Probability mass function (p.m.f.) x p(x) 1 p(x=1)=1/6 2 p(x=2)=1/6 3 p(x=3)=1/6 4 p(x=4)=1/6 5 p(x=5)=1/6 6 p(x=6)=1/6 x p(x) 1/6 1 2 3 4 5 6 ∑ = all x P(x) 1 Example 1a roll of a die
Cumulative distribution function(CDF) X P(xsA) 1 PX≤1F1/6 2 PX≤2F2/6 1.0 P() 5/6 3 PX≤3上=3/6 2/3 1/2 4 P(XS4F416 1/3 6 5 P(xS5516 123456 6 PX≤66/6
Cumulative distribution function (CDF) x P(x) 1/6 1 2 3 4 5 6 1/3 1/2 2/3 5/6 1.0 x P(x≤A) 1 P(x≤1)=1/6 2 P(x≤2)=2/6 3 P(x≤3)=3/6 4 P(x≤4)=4/6 5 P(x≤5)=5/6 6 P(x≤6)=6/6