According to the information in this post, we know that $ {\displaystyle z={\sqrt {-2\ln U_{1}}}\cos(2\pi U_{2})}$ follows a normal distribution, and the datas generated supports this view.

`data = Table[Sqrt[-2 Log[RandomReal[]]] Cos[2 π RandomReal[]], 10000]; ListPlot[data // BinCounts[#, {Min[data], Max[data], 0.05}] &, PlotRange -> All] `

But the following code can’t plot the probability density function of $ {\displaystyle z={\sqrt {-2\ln U_{1}}}\cos(2\pi U_{2})}$ , and I want to know how to solve it, even if the numerical approximation is used.

` dist = TransformedDistribution[ Sqrt[-2 Log[U1]] Cos[2 π U2], {U1 \[Distributed] UniformDistribution[{0, 1}], U2 \[Distributed] UniformDistribution[{0, 1}]}] Plot[PDF[dist, z], {z, 0, 1}, Filling -> Axis] `