Summary of the subject (topics) 1. Brief review of probability a. Example applications 2. Brief review of random variables a. Example applications 3. Brief review of random processes a. Classical description b. State space description

which we define as the correlation. Often we do not know the complete distribution, but only simple statistics. The most common of the moments of higher ordered distribution functions is the covarance

This is the main reason why use of the characteristic function is convenient This would also follow from the more devious reasoning of the density function for the sum of n independent random variables being the nth order convolution of the individual density functions-and the knowledge that convolution in the direct variable domain becomes multiplication in the transform domain

If a set of random variables X, having the multidimensional normal distribution is uncorrelated(the covariance matrix is diagonal, they are independent. The argument of the exponential becomes the sum over i of Thus, the distribution becomes a product of exponential

Non-zero power at non-zero frequency If R(r) includes a sinusoidal component corresponding to the component x()=Asin(o41+6) where 0 is uniformly distributed over 2t, A is random independent of 0, that component will be

where is the linearized system matrix. But this requires the full(same number of equations as finite differencing). In =time when the nominal trajectory

Last time: Ergodic processes An ergodic process is necessarily stationary. Example: Binary process

so if t is the current time in a real time situation, we cannot compute ()for which is necessary since w, () is nonzero only for>0. But we showed earlier that

System parameters are contained in,(t) and(t) Desired output is generated by taking the signal through the desired operator. The difference between the actual output and the desired output is the error, whose mean squared value we want to minimize We require a stable and realizable system. The error e(t) is given by:

天津大学：《建筑工程概预算》课程教学资源（PPT课件讲稿）土石方工程