MediumCalculusca-258

Density Under Linear Change of Variables

Problem

If X is normal with mean mu and standard deviation sigma, and Y = a*X + b with a != 0, then p_Y(y) = (1 / |a|) * phi((y - b) / a), where phi is the standard normal density.

Given y, mu, sigma > 0, a != 0, and b, return p_Y(y).

Hint

The absolute scale factor keeps the transformed density integrated to one for shrinking maps.

Test cases

case 1

in: [0,0,1,1,0]

expected: 0.3989422804014327

case 2

in: [0,0,1,2,0]

expected: 0.19947114020071635

case 3

in: [1,0,1,2,1]

expected: 0.19947114020071635

case 4

in: [0,0,1,-1,0]

expected: 0.3989422804014327

Starter codePython

def density_linear_transform(y, mu, sigma, a, b):
    # Your code here
    pass

4 test cases · run your code against them in the editor