Question 10.6.2: Batting statistics are often displayed as in Table 3. Use th...

Linear Algebra and Its Applications

Batting statistics are often displayed as in Table 3. Use the data in Table 3 to obtain the transition probabilities for the 2002 Atlanta Braves.

TABLE 3 Atlanta Braves Batting Statistics—2002 Season
Outs	Home Runs	Triples	Doubles	Singles	Hit Batsman	Walks
4067	164	25	280	959	54	558

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The sum of the entries in Table 3 is 6107. This is the total number of times that Atlanta Braves players came to bat during the 2002 baseball season. From the first two columns, there are 612 walks or hit batsmen. So, $p_{W}=612 / 6107=.1002$ . Of the 6107 times a player came to bat, a player hit a single 959 times, so $p_{1}=959 / 6107=$ .1570. Similar calculations provide $p_{2}=.0458, p_{3}=.0041, p_{H}=.0269, \text { and } p_{O}=$ .660. These values are placed in the matrices to produce the transition matrix for the Markov chain.

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