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Misc 4 - Given that x is mean and is variance of n observations - Miscellaneous

Misc 4 - Chapter 15 Class 11 Statistics - Part 2
Misc 4 - Chapter 15 Class 11 Statistics - Part 3 Misc 4 - Chapter 15 Class 11 Statistics - Part 4

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Misc 4 Given that is the mean and 2 is the variance of n observations 1 , 2 , 3 , ..., . Prove that the mean and variance of the observations 1 , 2 , 3 , ..., are a and a2 2, respectively (a 0). Given observations are 1 , 2 , 3 , ..., and be their mean and 2 is the variance Fro new observations, each observation is multiplied by a Let the new observations be 1 , 2 , 3 , ..., where = a( ) Calculating new mean New mean = 1 = 1 = a 1 = a So, New Mean = a Calculating new variance New Variance = 1 n ( ) 2 Now, Old Variance = 1 ( ) 2 2 = 1 ( ) 2 2 = ( ) 2 ( ) 2 = 2 ( 1 1 ) 2 = 2 1 2 ( ) 2 = 2 ( ) 2 = 2 a2 So, New Variance = 1 ( ) 2 = 1 2 a2 = 2 a2 Hence, New mean = a & New variance = 2 a2 Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.