NN=10000;

xNorm=Table[RandomReal[NormalDistribution[0,3]],{NN}];

Mean[xNorm]

Variance[xNorm]

xyNorm=Table[
{RandomReal[NormalDistribution[0,3]],RandomReal[NormalDistribution[0,3]]}
,{NN}];

ListPlot[xyNorm]

rOfXY[{x_,y_}]:=(x^2)+(y^2)

rValues=Map[rOfXY,xyNorm]

Histogram[rValues] (*variance of 9*)

Histogram[rValues] (*variance of 4*)

xyNorm=Table[
{RandomReal[NormalDistribution[0,1]],RandomReal[NormalDistribution[0,1]]}
,{NN}];

ListPlot[xyNorm]

A={{1,4},{-2,6}};

A //MatrixForm

A.{1.3,5.2}

Map[(A.#)&,xyNorm]

ListPlot[%]

Demo of CLT (Unis)

unis1=Table[Random[],{NN}];

Histogram[unis1]

unis2=Table[Random[],{NN}];

sum2=unis1+unis2;

Histogram[sum2]

unis3=Table[Random[],{NN}];

sum3=unis1+unis2+unis3;

Histogram[sum3]

Demo of CLT (Exps)

exps1=Table[RandomReal[ExponentialDistribution[1]],{NN}];

Histogram[exps1]

exps2=Table[RandomReal[ExponentialDistribution[1]],{NN}];

sum2=exps1+exps2;

Histogram[sum2]

exps3=Table[RandomReal[ExponentialDistribution[1]],{NN}];

sum3=exps1+exps2+exps3;

Histogram[sum3]