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Unformatted text preview: = P [ X i +1 = 2  X i = 1 , Y i = H ] P [ Y i = H  X i = 1] + P [ X i +1 = 2  X i = 1 , Y i = T ] P [ Y i = T  X i = 1] = 0 + 1 × . 3 = 0 . 3 P 21 = P [ X i +1 = 1  X i = 2] = P [ X i +1 = 1  X i = 2 , Y i = H ] P [ Y i = H  X i = 2] + P [ X i +1 = 1  X i = 2 , Y i = T ] P [ Y i = T  X i = 1] = 1 × . 6 + 0 = 0 . 6 P 22 = P [ X i +1 = 2  X i = 2] = P [ X i +1 = 2  X i = 2 , Y i = H ] P [ Y i = H  X i = 2] + P [ X i +1 = 2  X i = 2 , Y i = T ] P [ Y i = T  X i = 2] = 0 + 1 × . 4 = 0 . 4 The transition matrices are P = ± . 7 0 . 3 . 6 0 . 4 ² P 3 = ± . 667 0 . 333 . 666 0 . 334 ² The probability that coin 1 is ﬂipped on the third day is 1 2 ( P 3 11 + P 3 21 ) = 0 . 666. 2...
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 Fall '08
 Lim
 Operations Research, weather, Yi, Rain, Nikon Coolpix S3, S3 Graphics

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