Leave N alone a hypergeometric irregular variable having the dispersion ot the quantity of white balls in

an irregular example of size r trom a set ot w white and b blue balls. That is, the place where we utilize the

show that (m) O' if eitherj< O or j > m. Presently, considera compound arbitrary variable

SN = X, : , where the X/are positive number esteemed irregular factors with q = P{Xi = D.

PIN

(a) With Mas characterized as in Section 3.7, discover the conveyance of M-1.

(b) Suppressing its reliance on b: let PW r (k) = P{SN = k}, and infer a recursion condition

for PW r(k).

(c) Lise the recursion of (5) to discover P

58))

For a Markov chain (Xn,n > O) with change probabilities Pi j, consider the contingent

likelihood that given thatXn = m the chain began at time 0 in state I and has not yet entered

state r by time n, where r is a predefined state not equivalent to possibly I or m. We are keen on

regardless of whether this contingent likelihood is equivalent to the n stage progress likelihood ota Markov chain

whose state space does exclude state r and whose change probabilities are

Either demonstrate the uniformity

or on the other hand develop a counterexample.

59))

Coin 1 comes up heads with likelihood 0.6 and coin 2 with likelihood 0.5. A coin is constantly

flipped until it comes up tails, at vvhich time that coin is set to the side and we sta flipping the other

one.

(a) What extent of flips use coin 1?

(b) It we start the cycle with coin 1 what is the likelihood that coin 2 is utilized on the fifth flip?

(c) What extent of lips land heads?

60))

A progress likelihood network P is supposed to be doubly stochastic if the total over every segment

rises to one; that is:

Pij=l,

for all j

It such a chain is final and comprises of M + 1 states O, 1, .

extents are given by

1

M, show that the since a long time ago run