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