A spaceship is trying to land on the planeR2. It chooses it's place of landing by first randomly generating a radiusR according a continuous distribution and density function fR.

OnceR is decided, the spaceship will choose the landing point(X,Y) uniformly at random inside the disc centred at(0,0) with radius R.

Find a density functionfR so that(X,Y) has the standard Gaussian distribution on R2. Justify your answer.

[7 marks] A spaceship is trying to land on the plane R2. It chooses it's place of landing by first randomly generating a radius R according a continuous distribution and density function f3. Once R is decided, the spaceship will choose the landing point (X, Y) uniformly at random inside the disc centred at (0,0) with radius R. Find a density function fR so that (X, Y) has the standard Gaussian distribution on R2. Justify your