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HW3 - Physics 132 Homework 3 Consider a set of N equivalent...

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Physics 132 Homework 3 Consider a set of N equivalent measurements of a quantity x (each measurement being labeled with a subscript x i ) which we assume contain random errors. Assume the usual normalized model for the probability distribution for each measurement: ( ) 2 2 1 ( ) exp( ) 2 2 i i x f x μ σ πσ = Also, use the usual definition for the expectation value for a function 1 2 ( , ,..., ) N P x x x which can depend on all of the measurements: ( ) 1 2 1 2 1 2 ... ( , ,..., ) ( ) ( )... ( ) ... N N N P P x x x f x f x f x dx dx dx ∫∫ ∫ Show that: 2 2 1 ( ) ( 1) N i i x x N σ = = The average value of the measurements, x , is also defined in the usual way:
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