Stochastic

# Suppose there are n extreme points and they are

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Unformatted text preview: ? (b) What is the expected time until a trainee auits or becomes supervisor? 1.65. Customers shift between variable rate loans (V), thirty year ﬁxed-rate loans (30), ﬁfteen year ﬁxed-rate loans (15), or enter the states paid in full (P), or foreclosed according to the following transition matrix: V V .55 30 .15 15 .20 P 0 F 0 30 .35 .54 0 0 0 15 0 .25 .75 0 0 P f .05 .05 .05 .01 .04 .01 1 0 0 1 (a) For each of the three loan types ﬁnd (a) the expected time until paid or foreclosed. (b) the probability the loan is paid. 1.66. Brother–sister mating. In this genetics scheme two individuals (one male and one female) are retained from each generation and are mated to give the next. If the individuals involved are diploid and we are interested in a trait with two alleles, A and a, then each individual has three possible states AA, Aa, aa or more succinctly 2, 1, 0. If we keep track of the sexes of the two individuals the chain has nine states, but if we ignore the sex there are just six: 22, 21, 20, 11, 10, and 00. (a) Assuming that reproduction corresponds to picking one letter at random from each pare...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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