Sum of squares of uniformly distributed variables











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Let X, from which I draw N samples, have a uniform distribution on $(-1,1)$. What is the distribution of the sum of squares -- $sumlimits_{i=0}^{N-1} {x_i}^2$ -- and its variance? We can assume N to be very large.










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Let X, from which I draw N samples, have a uniform distribution on $(-1,1)$. What is the distribution of the sum of squares -- $sumlimits_{i=0}^{N-1} {x_i}^2$ -- and its variance? We can assume N to be very large.










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  • Please include your own thoughts, the effort made so far, and the specific difficulties you faced that got you stuck. Otherwise this question is likely to be closed via community votes or just be ignored.
    – Lee David Chung Lin
    Nov 15 at 14:35













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up vote
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down vote

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Let X, from which I draw N samples, have a uniform distribution on $(-1,1)$. What is the distribution of the sum of squares -- $sumlimits_{i=0}^{N-1} {x_i}^2$ -- and its variance? We can assume N to be very large.










share|cite|improve this question













Let X, from which I draw N samples, have a uniform distribution on $(-1,1)$. What is the distribution of the sum of squares -- $sumlimits_{i=0}^{N-1} {x_i}^2$ -- and its variance? We can assume N to be very large.







probability probability-distributions uniform-distribution






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asked Nov 14 at 20:35









Bjorn

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  • Please include your own thoughts, the effort made so far, and the specific difficulties you faced that got you stuck. Otherwise this question is likely to be closed via community votes or just be ignored.
    – Lee David Chung Lin
    Nov 15 at 14:35


















  • Please include your own thoughts, the effort made so far, and the specific difficulties you faced that got you stuck. Otherwise this question is likely to be closed via community votes or just be ignored.
    – Lee David Chung Lin
    Nov 15 at 14:35
















Please include your own thoughts, the effort made so far, and the specific difficulties you faced that got you stuck. Otherwise this question is likely to be closed via community votes or just be ignored.
– Lee David Chung Lin
Nov 15 at 14:35




Please include your own thoughts, the effort made so far, and the specific difficulties you faced that got you stuck. Otherwise this question is likely to be closed via community votes or just be ignored.
– Lee David Chung Lin
Nov 15 at 14:35















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