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Unformatted text preview: STA 100 Lecture 15 Paul Baines Department of Statistics University of California, Davis February 7th, 2011 Admin for the Day I Please pick up Midterm+old homeworks I Important: Homework 3 Solutions posted please read! I Homework 4 posted, due Wednesday by 5pm! I Hwk 4, Q2(i) compare to the correct answer for Hwk3 Q2(k) I Hwk 4, Q3 Weekly data (not monthly) I Project details coming soon. . . Admin for the Day I Please pick up Midterm+old homeworks I Important: Homework 3 Solutions posted please read! I Homework 4 posted, due Wednesday by 5pm! I Hwk 4, Q2(i) compare to the correct answer for Hwk3 Q2(k) I Hwk 4, Q3 Weekly data (not monthly) I Project details coming soon. . . References for Today: Rosner, Ch 6.56.8, Ch 6.5 (7th Ed.) References for Wednesday: Rosner, Ch 6.56.8 (7th Ed.) Recap: Linear Combinations We just covered linear transformations , where you add and multiply a single random variable by fixed numbers ( a and b ). Now we consider linear combinations of random variables. This is where you add multiple random variables together. . . Recap: Linear Combinations We just covered linear transformations , where you add and multiply a single random variable by fixed numbers ( a and b ). Now we consider linear combinations of random variables. This is where you add multiple random variables together. . . These are different things! Linear transformations deal with transformations of a single variable (usually to change units), whereas linear combinations deal with what happens when you combine lots of random variables (usually to take a sum or average of them). Recap: Linear Combinations Let X 1 ,..., X n be any random variables, c 1 ,..., c n constants (just numbers). Recap: Linear Combinations Let X 1 ,..., X n be any random variables, c 1 ,..., c n constants (just numbers). I The mean of a linear combination of any random variables: E [ c 1 X 1 + c 2 X 2 + + c n X n ] = c 1 E [ X 1 ] + c 2 E [ X 2 ] + + c n E [ X n ] . I The variance of a linear combination of independent random variables: Var ( c 1 X 1 + c 2 X 2 + + c n X n ) = c 2 1 Var ( X 1 ) + c 2 2 Var ( X 2 ) + + c 2 n Var ( X n ) . I The SD of a linear combination of independent random variables: compute the variance and take a square root. Note: you cannot just add the standard deviations! I Linear combinations of normally distributed random variables are still normally distributed! Recap: Linear Combinations Let X 1 ,..., X n be independent normally distributed random variables, c 1 ,..., c n constants (just numbers). I If we create a new random variable using the X s, say: Y = c 1 X 1 + c 2 X 2 + + c n X n , then, using the properties on the previous slide we get: Recap: Linear Combinations Let X 1 ,..., X n be independent normally distributed random variables, c 1 ,..., c n constants (just numbers)....
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This note was uploaded on 03/09/2011 for the course STAT 100 taught by Professor drake during the Spring '10 term at UC Davis.
 Spring '10
 DRAKE
 Statistics

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