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lec4 - BUAD 310 G MUKHERJEE FALL 2013 LECTURE 4 OUTLINE v...

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BUAD 310 G. MUKHERJEE FALL 2013: LECTURE 4
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OUTLINE v Probability Problem Solving: Based on addition rules & multiplication rules of Lecture 3. v Chapter 9: Random Variables [r.v.] ü De#inition & Examples o Discrete & Continuous Random variables ü On Attributes of Random Variables o Expected Value, Variance & the Sharpe Ratio This Lecture: Mostly discrete random variable ; Chapter 12: Continuous random variable [next week]
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PROBLEM 1 v For a multiple choice question with 4 options what is the probability of getting the correct answer by randomly clicking on an option? v You take a quiz with 5 such multiple-­‐choice questions. What’s the chance of getting all correct answers? q What assumptions do you make for getting the answer?
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MAIN DIFFICULTY IN PROBABILITY PROBLEMS What rule should I use? (a) Addition (b)Multiplication v Addition q Through Venn diagrams; q Disjoint events & modidied rule for overlapping ones. v Multiplication: Sequential Decision making q independent sequence of decisions. q conditional decision making : to dind the probabilities of successive events, multiply conditional probabilities given the previous events.
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MAIN DIFFICULTY IN PROBABILITY PROBLEMS What rule should I use? v Addition: Venn diagrams [Disjoint or Overlapping] v Multiplication: Sequential Decision making v Both: In decision trees q Step 1: decompose the event into disjoint sub-­‐events. q Step 2: Get probability of each of those sub-­‐events separately by using multiplication rule on the conditional probabilities in the tree. q Step 3: Add the probabilities of the sub-­‐events of step 1.
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PROBLEM 2 v Probability that it will rain tomorrow if it rains today is 0.8. v Probability that it will rain tomorrow if it does not rains today is 0.1. v The probability that it will rain today is 0.6. q What is the chance that it will rain tomorrow? ü Draw the decision tree first?
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PRACTICE PROBLEM 1 v A fair die is thrown twice. Calculate: q P(least one of the throws is a 3)?
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