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V expected value variance 108 notes expected value and

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Unformatted text preview: Variable (r.v.) Expected Value Variance 10.8 Notes Expected Value and Variance Example 32 Notes Suppose X and Y are random variables with E[X ] = 3, E[Y ] = 4 and Var (X ) = 4. Find: 1 E[2X + 1] 2 E[X − Y ] Random Variable (r.v.) 3 E[X 2 ] Expected Value 4 E[X 2 Variance 5 E[(X − 4)2 ] 6 Var (2X − 4) − 4] 10.9 Expected Value and Variance Example 32 Solution. 1 E[2X + 1] = 2 × E[X ] + 1 = 7 2 E[X − Y ] = E[X ] − E[Y ] = 3 − 4 = −1 Random Variable (r.v.) 3 E[X 2 ] = Var (X ) + (E[X ])2 = 4 + 9 = 13 Expected Value 4 E[X 2 5 6 − 4] = E[X 2 ] −4=9 Variance E[(X − 4)2 ] = Var (X − 4) + (E[X − 4])2 = Var (X ) + (E[X − 4])2 = 4 + 1 = 5 Var (2X − 4) = Var (2X ) = 22 × Var (X ) = 16 10.10 Notes...
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This note was uploaded on 01/24/2014 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue.

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