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Chapter 6

# Chapter 6 - Chapter6 KVANLI PAVUR KEELING Discrete...

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Click to edit Master subtitle style   Chapter 6 Discrete  Probability  Distributions KVANLI PAVUR KEELING

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3/13/11 Chapter Objectives v At the completion of this chapter, you should be able to answer the following questions: ∙ What is meant by the term " probability distribution ?" ∙ What is the formula for the mean and variance
3/13/11 Discrete Random Variable A random variable X is a function that assigns a numerical value to each outcome of an experiment. A discrete random variable is a random variable whose values are counting numbers or discrete data

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3/13/11 Example v How many outcomes we can get if we flip a coin once? v http:// www.youtube.com/watch?v=x30zecUW v How about we flip a coin twice? 3 times? v Suppose we’re interested in the number of heads in the 2 flips
3/13/11 Example v Chances of getting exactly one H in the 2 flips is P(B or C) = P(B) + P(C) since B and C are mutually exclusive v P(B) = P(H on 1st flip and T on 2nd flip) = P(H on 1st flip) · P(T on 2nd flip)

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3/13/11 An Easier Way v Define X to be the number of H’s in the 2 flips 0 with probability X = 1 with probability 2 with probability X=0 How can this occur? T on 1st flip and T on 2nd flip For a fair coin, this is ½ · ½ since coin flips are independent
3/13/11 Defining the Random Variable 0 with probability X = 1 with probability 2 with probability X=1 How can this occur? H on 1st flip and T on 2nd flip - OR - T on 1st flip and H on 2nd flip P(X = 1) is ¼ + ¼ = ½ ¼ As before, this is ½ · ½ = ¼ And this is ½ · ½ = ¼

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3/13/11 Defining the Random Variable 0 with probability X = 1 with probability 2 with probability X=2 How can this occur? H on 1st flip and H on 2nd flip P(X = 2) is ½ · ½ = ¼ ¼ Once again, this is ½ · ½ = ¼ ½ ¼
3/13/11 A Discrete Random Variable v X = number of H’s in 2 coin flips is called a discrete random variable v Why discrete ? v Suppose you observe X v You would get something like {1, 1, 0, 2, 1, 2, 0, 1, …,1} v These are discrete data. X = (counting something) This is a sample

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3/13/11 Continuous Random Variable v The other type of random variable is a continuous random variable v Here , X = (measuring something) v Examples: Height, weight, length, length of time v Consider a sample of heights: {5.82’, 6.45’,…., 5.41’} v These are continuous data
3/13/11 Another Discrete Random Variable Container with 30 poker chips 10 of these 10 of these 10 of these 1 2 3 Select 2 chips with replacement Let X = total of the 2 chips

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3/13/11 X = Total of the 2 Chips 2 with probability 3 with probability X = 4 with probability 5 with probability 6 with probability X=2 How can this occur? on the 1st draw and on the 2nd draw The probability of selecting a on each draw is 1/3 since 10 of the 30 chips are numbered one v P(X = 2) is ⅓ · ⅓ = 9 1 Remember: We replace the 1st chip before drawing the 2nd chip
X = Total of the 2 Chips 2 with probability 3 with probability X = 4 with probability 5 with probability

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Chapter 6 - Chapter6 KVANLI PAVUR KEELING Discrete...

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