工程数学(三)概率统计 离散数学（Engineering Mathematics (three) discrete mathematics of probability and statistics）.doc

工程数学(三)概率统计 离散数学（Engineering Mathematics (three) discrete mathematics of probability and statistics） The third chapter random variable and its distribution If we care about the event A={no defective}, B={has at least 2 defective}, C={no more than k defective}, then A, B, C can be expressed as random variable Y respectively A={e|Y (E) =0}, B={e|Y (E) = 2}, C={e|Y = k}. (E) For the sake of convenience, generally in the event that can save e, so it can be expressed as B={Y = 2} A={Y=0} exergy exergy, exergy exergy value, C={Y = k}. random variables varies with the test results, it can not predict what value before the experiment, and it has a certain value for the random probability variable and ordinary function is essentially different. The introduction of random variables enables us to use random variables to describe various stochastic phenomena, so it is possible to study the results of random trials by calculus The distribution function of 2. random variables Definition 3.2 let X be a random variable, X is the function of any real number and the function value on [0, 1] F (x) =P (X = x), - - x+ - It is called the distribution function of random variable X For arbitrary x 1, x 2 (x 1x 2, a) P (x 1X x = 2) =P (X = x 2) -P (X = x =F (1) x (x 2) -F 1 (3.1)). Therefore, if the distribution function of the known X, X know any fall in the interval (x 1, 2 probability on the X in this sense, the distribution function of a complete description of the statistical regularity of random variables. The distribution function is a general function, and it can be used to study random variables by calculus If the X is regarded as the axis of random point coordinates, then the distribution function F (x) x in the function value at that X falls in the range of X (probability on the infty,. 3.3 cases of a random variable X of all possible values for X 1=-1, X 2=2, X 3=3. event {X = x i} (i=1,2,3) probability for exergy exergy P (X = -1 = 1 = 14) p, P (X = 2) = P 2 = 12, P (X = 3) =