Understanding the Normal Distribution pdf and cdf

Supplement to Lecture 6

npdf =  
      Function[{x, μ, σ},  (1/(σ (Sqrt[ 2 π]))) (E^(-(((x - μ))^2)/(2  (σ^2))))]

npdf01  =  Function[{x},  npdf[x, 0, 1]]

Plot[npdf01[x], {x , -5,  5}]

npdf04 =  Function[{x},  npdf[x, 0, 4]]

Plot[npdf04[x], {x , -10,  10}]

ncdf  =  
      Function[{y, μ, σ}, (∫_(-∞)^y) npdf[
              x, μ, σ] \[DifferentialD]x]

ncdf01  =   Function[{y}, 
        ncdf[y, 0, 1] ]

Plot[npdf01[x],  {x, -3, 3}]

Plot[ncdf01[y], {y, -3, 3}]

ncdf01[0]