2. 2.5/10.5 pointsI Previous Answers My Notes Ask Your Teach Paul travels back a

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2. 2.5/10.5 pointsI Previous Answers My Notes Ask Your Teach Paul travels back and forth in his work between New York and Boston. He never makes two trips on the same day. On a day when he wakes up in New York, the probability is 0.04 that he will fly to Boston during the day. On a day when he wakes up in Boston, the probability is 0.11 that he will fly to New York. Use this information to create a transition matrix, using the row labels as shown below New YorkBoston New York 0.95 0.04 0.11 0.89 Use this T matrix to answer the following questions (a) If Paul wakes up in Boston on Monday, what is the probability he will wake up in New York on Wednesday? (Hint: Going from Monday to Wednesday is equivalent to moving forward in time two days: Monday to Tuesday then Tuesday to Wednesday.) 0.12728 x (b) If Paul wakes up in New York on Monday, what is the probability he will wake up in New York on Wednesday? 0.12728X (c) If Paul wakes up in New York on Monday, what is the probability he will wake up in Boston on Thursday? 0.12728X (d) If Paul wakes up in Boston on Monday, what is the probability he will wake up in Boston on Thursday?

Explanation / Answer

solution=

On any day Paul wakes up in New York
P(Paul wakes up in Boston next day) = 0.04 -----> given
P(Paul wakes up in New York next day) = 0.96

On any day Paul wakes up in Boston
P(Paul wakes up in New York next day) = 0.11 -----> given
P(Paul wakes up in Boston next day) = 0.89

a)

If Paul wakes up in Boston on Monday:

P(Paul wakes up in New York on Wednesday)
= P(Paul wakes up in Boston on Tuesday, and in N.Y. on Wednesday)
+ P(Paul wakes up in N.Y. on Tuesday and in N.Y. on Wednesday)

= P(BB) * P(BN.Y.) + P(BN.Y.) * P(N.Y.N.Y.)
= (0.89 * 0.11) + (0.11 * 0.96)
= 0.2035

b)

If Paul wakes up in New York on Monday:

P(Paul wakes up in New York on Wednesday)
= P(Paul wakes up in Boston on Tuesday, and in N.Y. on Wednesday)
+ P(Paul wakes up in N.Y. on Tuesday and in N.Y. on Wednesday)

= P(N.Y.B) * P(BN.Y.) + P(N.Y.N.Y.) * P(N.Y.N.Y.)
= (0.04 * 0.11) + (0.96 * 0.96)
= 0.9260

c)

If Paul wakes up in New York on Monday:

P(Paul wakes up in New York on Thursday)
= P(Paul wakes up in N.Y. on Wednesday) * P(N.Y.N.Y.)
+ P(Paul wakes up in Boston on Wednesday) * P(BN.Y.)

= (0.9260 * 0.96) + ((10.9260) * 0.11)
= 0.8971

d)

If Paul wakes up in Boston on Monday

P(Paul wakes up in Boston on Thursday)
= P(Paul wakes up in N.Y. on Wednesday) * P(N.Y.B)
+ P(Paul wakes up in Boston on Wednesday) * P(BB)

= (0.2035 * 0.04) + ((10.2035) * 0.89)
= 0.7170

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