Math 203_Lecture 8

Math 203_Lecture 8 - Principles of Statistics 1 Lecture 8:...

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Principles of Statistics 1 Lecture 8: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 12, 2011
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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4:
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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 .
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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 . Wanted to calculate P (270 X 290)
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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 . Wanted to calculate P (270 X 290) The table for Binomial in the back of the text book DOES NOT HAVE the case n = 800 .
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Approximating a Binomial distribution Remember the Food and Drug Administration (FDA) example in Lecture 15, Chapter 4: We had a Binomial random variable X with parameters n = 800 and p = 0 . 35 . Wanted to calculate P (270 X 290) The table for Binomial in the back of the text book DOES NOT HAVE the case n = 800 . Can we approximate the above probability?
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Histograms of the Bin(800, 0.35) Binom(800,0.35) y Frequency 240 260 280 300 320 0 500 1000 1500
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Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric.
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Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Can we approximate the distribution of the X by a normal distribution?
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Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Can we approximate the distribution of the X by a normal distribution? Note that if X Bin ( n,p ) then μ = E ( X ) = n × p , σ 2 = V ar ( X ) = n × p × (1 - p ) .
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Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Can we approximate the distribution of the X by a normal distribution? Note that if X Bin ( n,p ) then μ = E ( X ) = n × p , σ 2 = V ar ( X ) = n × p × (1 - p ) . in our example the values are μ = 800 × 0 . 35 = 280 , σ 2 = 800 × 0 . 35 × 0 . 65 = 182
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Approximating a Binomial distribution As you can see the distribution of the Binomial under consideration is mound-shaped and symmetric. Can we approximate the distribution of the X by a normal distribution?
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This note was uploaded on 07/15/2011 for the course MATH 203 taught by Professor Dr.josecorrea during the Summer '08 term at McGill.

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Math 203_Lecture 8 - Principles of Statistics 1 Lecture 8:...

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