一、实验大纲 二、实验指导书 三、教学大纲

In the special case when E's are conditionally independent(though they all depend on the alternative, Ak), P(, E2..)= P(A... -)P() ()P) This is easy to do and can be done recursively

16.322 Stochastic Estimation and Control Professor Vander Velde 1. P(ABCD.=P(A)P(B A)P(C|AB)P(D 1 ABC) Derive this by letting A=CD. Then P(BCD)= P(CD)P(B ICD)= P(C)P(DIC)P(DICD) 2. If A,, A2r.. is a set of mutually exclusive and collectively exhaustive events, then

The Poisson approximation to the binomial distribution The binomial distribution, like the Poisson, is that of a random variable taking only positive integral values. Since it involves factorials, the binomial distribution is not very convenient for numerical application

Direct determination of the joint probability density of several functions o several ra andom variables Suppose we have the joint probability density function of several random variables x, Y, Z, and we wish the joint density of several other random variables defined as functions xyz

Mean squared value: Higher order distribution and density functions. You can define these distributions of any order

Prof vander Velde Use error between early and late indicator to lock onto signal. Error is a linear function of shift, within the range (-T,T) Return to the 1 st example process and take the case where the change points are Poisson distributed

Note that in the case of repeated roots of the denominator, a pole of multiple order contributes only a single residue. To evaluate F(s)ds by integrating around a closed contour enclosing the entire left half plane, note that if F()0 faster than-for large s, the integral along the curved part of the contour is zero

Note n, s enter the system at the same place F is fixed. We design(and perhaps B). We must stabilize F if it is given as unstable

For the differential system characterized by its equations of state,specialization to invariance means that the system matrices A, B,C are constants