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plant paradise • jenga • therapy dogs • exh -“auction”

STA107. Monday April 7 th. 10:00am – 12:00pm. IB 3 45. plant paradise • jenga • therapy dogs • exh -“auction”. free healthy snacks • study space • live music • crafts . tea • appreciation cards • exam prep • sneaker squad . www.fb.com/utmExamJam.

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plant paradise • jenga • therapy dogs • exh -“auction”

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  1. STA107 Monday April 7th 10:00am – 12:00pm IB 345 plant paradise • jenga • therapy dogs • exh-“auction” free healthy snacks • study space • live music • crafts tea • appreciation cards • exam prep • sneaker squad www.fb.com/utmExamJam www.utm.utoronto.ca/exam-jam

  2. 0.1 0.9 0.8 coke pepsi 0.2 Example • Given that a person’s last cola purchase was Coke, there is a 90% chance that his next cola purchase will also be Coke. • If a person’s last cola purchase was Pepsi, there is an 80% chance that his next cola purchase will also be Pepsi. STA107 Lecture 26Markov Chain Probabilities transition matrix:

  3. Given that a person is currently a Pepsi purchaser, what is the probability that he will purchase Coke two purchases from now? Pr[ Pepsi?Coke ] = Pr[ PepsiCokeCoke ] +Pr[ Pepsi Pepsi Coke ] = 0.2 * 0.9 + 0.8 * 0.2 = 0.34 ?  Coke Pepsi ?

  4. Given that a person is currently a Coke purchaser, what is the probability that he will purchase Pepsithree purchases from now?

  5. Assume each person makes one cola purchase per week • Suppose 60% of all people now drink Coke, and 40% drink Pepsi • What fraction of people will be drinking Coke three weeks from now?

  6. k Step Transition probabilities p(k)(ij) = P(Xn+k = j|Xn = i) • entry i,j in the matrix Pk gives k-step transition probabilities, p(k)(ij)

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