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:

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

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

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

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

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

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

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

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

1.掌握本量利分析的主要内容 2.了解分部报告产生的原因 3.掌握责任中心的主要类型及其考核方式 4.掌握业绩评价的主要方法 5.了解转移价格对内部考核的影响 6.了解预算的主要作用