Probability and Statistics(6/35) Concepta酸 To calculate this in MATLAB,one can use the function called mean.If the argument to this function is a matrix,then it provides a vector of means,each one corresponding to the mean of a column. > One can find the mean along any dimension (dim)of multi- dimensional arrays using the syntax:mean(x,dim) IfX=[012,345]; then mean (X,1)is[1.52.53.5] CPHAW and mean (X2)is[1;4] @月停大学 TONGJI UNIVERSITY
If X = [0 1 2; 3 4 5]; then mean (X,1) is [1.5 2.5 3.5] and mean (X,2) is [1; 4] ➢ To calculate this in MATLAB, one can use the function called mean. If the argument to this function is a matrix, then it provides a vector of means, each one corresponding to the mean of a column. ➢ One can find the mean along any dimension (dim) of multidimensional arrays using the syntax: mean(x, dim). Probability and Statistics(6/35) Concept
Probability and Statistics(7/35) Concept The variance of a random variable is given by the following definition. G2=V(X)E[(X-u)]=f(x-u)f(x)dx We note that equation can also be written as: V(X)=E[X2]-u2=E[X2]-(E[X])2 @日济大学 AW TONGJI UNIVERSITY
➢ The variance of a random variable is given by the following definition. We note that equation can also be written as: Probability and Statistics(7/35) Concept
Probability and Statistics(8/35) Concept These statistics can be calculated in MATLAB using the functions std(x)and var(x),where x is an array containing the sample values. Similar to the function mean,these can have matrices or multi- dimensional arrays as input arguments. CDHAW @月协大学 TONGJI UNIVERSITY
➢ These statistics can be calculated in MATLAB using the functions std(x) and var(x), where x is an array containing the sample values. ➢ Similar to the function mean, these can have matrices or multidimensional arrays as input arguments. Probability and Statistics(8/35) Concept
Probability and Statistics(9/35) Axioms >Probabilities follow certain axioms that can be useful in computational statistics.We let S represent the sample space of an experiment and E represent some event that is a subset of S. The probability ofevent E must be between 0 and 1: 0≤P(E)≤1 P(S)=1 For mutually exclusive events: P(EE2...E)=>P(E i=1 @日济大学 AW TONGJI UNIVERSITY
Probability and Statistics(9/35) Axioms ➢ Probabilities follow certain axioms that can be useful in computational statistics. We let S represent the sample space of an experiment and E represent some event that is a subset of S. The probability of event E must be between 0 and 1: For mutually exclusive events:
Probability and Statistics(10/35 Axioms金a The conditional probability of event E given event F is defined as follows: EF):P(F) P(F) Here P(EF)represents the joint probability that both E and F occur together. We can rearrange this equation to get the following rule: P(E⌒F)=P(F)P(EIF) 细月济大学 TONGJI UNIVERSITY
➢ The conditional probability of event E given event F is defined as follows: Here represents the joint probability that both E and F occur together. We can rearrange this equation to get the following rule: Probability and Statistics(10/35) Axioms