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    "# Problem definition\n",
    "Tina Belcher, brand-new manager of the new Bob´s burger parlour downtown San Francisco,  wants to analyse the impact on the market and the loyalty of the customers of Bob’s Burger and Pesto´s, an Italian restaurant nearby. It is assumed that one customer dines once a week at Bob’s or at Pesto´s, but not at both.\n",
    "Tina has collected information from 100 consumers over a 10-week period. When checking the data, she discovered that of all the customers who consumed at Bob’s in a given week, 90 % returned to the restaurant following week, while 10 % switched to Pesto’s. Of all the consumers who consumed at Pesto’s in a given week, 80 % returned to the same place the following week, but 20 % switched to Bob´s.\n",
    "Assuming that the transition probabilities are the same for every customer and that they not change over time, we can get insights modelling customer fidelity with Markov chains.\n"
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    "Model customer fidelity as a Markov process and answer the following questions:\n",
    "\n",
    "**a)** If at week 0, a customer dines at Bob’s, what is the probability of the same customer dining at Bob´s in week 1?\n",
    "\n"
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    "**b)** What is the probability of a customer going back to Bob´s two weeks running?\n"
   ]
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   "source": [
    "**c)** What is the probability of a customer changing to Pesto´s after dining at Bob´s and then going back to Bob´s\n",
    "\n"
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   "source": [
    "**d)** Consider the customer of section a) what is the probability that this customer comes back to Bob´s in two weeks time?\n"
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   "source": [
    "**e)** What is the expected market share of customers between the two restaurants?"
   ]
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