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I've made a 2D walker to compare different RNG's. I'm measuring the succes of each walk as the distance from the origin to the endpoint, using the regular 2-norm. The thing I can't seem to work out is the variance.

[tex]D_n=\sqrt(x_n^2+y_n^2)[/tex]

[tex]Var(D_n)=E[D_n^2]=E[Z_1^2+...+Z_n^2][/tex]

Since [itex]Var(Z_i)=\sqrt{2}[/itex] does this mean that the variance is [itex]2n[/itex]? Seems too easy...

Ps. I'm not sure how to make the formatting prettier, if someone can tell me, I'll edit it naturally!

Ps2. Thanks Stephen Tashi!

[tex]D_n=\sqrt(x_n^2+y_n^2)[/tex]

[tex]Var(D_n)=E[D_n^2]=E[Z_1^2+...+Z_n^2][/tex]

Since [itex]Var(Z_i)=\sqrt{2}[/itex] does this mean that the variance is [itex]2n[/itex]? Seems too easy...

Ps. I'm not sure how to make the formatting prettier, if someone can tell me, I'll edit it naturally!

Ps2. Thanks Stephen Tashi!

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