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 is taking a stochastic process class and cach wek his prwoe e w eefioemance could the in one week, he won behind for each week. If he is above avernge average or behind in the next weeck with probability average in one week, he will be a If he is ge in one week, he will be above average or behind in the est nest week with probability 0 3 or o.2 respectively. . or 0.3 respectively. I be above average or behind in the mest weck with probability average in the next week with probability u.ge hext week with probability o.1 and 0.6 respectively To be "above average" is given as below It he is behind in one week, he willt be above average or model the problem, wo set state 2 to be "average", and state J to state 2 to be "average", and state 3 to be behind" The transition matris e two-step and three-step transition matrices are given as below P2 Th Th 0.390 0.430 0.450 0.250 0.270 0.290 360 0.260 0.264 0.414 0.424 0.432 0.270 0.322 0.306 0.294 pa 0.274

Explanation / Answer

Expected number of weeks tht he will be above averagge in the first three weeks=

1*probability of being above average in the first week+2*probability of being above average in the second week+3*probability of being above average in the third week

According to the transition matrix this is=1*0.1+2*0.260+3*0.294=1.502 weeks

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