# densities

1. ### Rescaling densities

Suppose I have some collection of discrete densities $\rho_i(n)$ defined on domains $D_i$ of differing lengths (assume one dimension). Is there some standard trick for rescaling each densities' domain so that they all have some fixed domain $D$? I guess you could modify the argument to each...
2. ### How to interpolate densities?

I have a density function $f_n(z)$ with vanishing mean and unit variance. It obeys a recursive integral relation: f_{n+1}(z) = \sqrt{(n+1)/n}\int_{-\infty}^{+\infty}f_n(z_n)f_0(\sqrt{n+1}z - \sqrt{n}z_n) dz_n I wish to find a reasonable method to continue n onto the positive reals by...
3. ### probability question: conditioning densities

Suppose X, Y are random variables with joint density f(x,y) = A^(3)xe^(-Ay) for 0<x<y = 0 otherwise a) What is the density of Y? What is E(Y)? b) What is E(X|Y=1)? -- thanks in advance for your help!