Note: Partial credit will be given if you i Total Points: 100 1. (25 points) Bob

Question

Note: Partial credit will be given if you i Total Points: 100 1. (25 points) Bob is taking a stochastic given if you indicate the correct approaeh. above average, average, or be average or behind in the nest average in one week, he wil 0.3 a stochastic process class and cach woek, his pefoesance could bs or behind for each weck If he is above average in one week he wsti weck. he et week with peobability 0 3 ce 0.2 respectively. If he s ill be above average or behind in the nest sweek with probsbiliy or average in the set state 1 or 0.3 respectively. If he is behind in one week, he will be ahsy next week with probability, "average". mext week with probability O. I and 0.6 respectively Tso be "above av model the problern, w The transition is given as below en as below te2 to be "average". and state 3 to be "behin The two-step and three-step transition matrices are given as below P2 .360 0.300 0.260 0.390 0.430 0.450 0.250 0.270 0.290 0.264 0.322 0.306 0.294 0.414 0.424 0.432 pa 0.270 0.274

Explanation / Answer

Given that Bob initially above average that is at State 1, then

the probability that he will be left behind (that is State 3) for the first time at week 2 = P^2 ( 1,3 ) = 0.25.

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