[AussieKenDoll]

why there is two relatively height 1 peaks and two relatively height 3 peaks as of 1:3:3:1?

[sjb]

Each proton splits the signal by ± 1/2. Consider this somewhat analogous to flipping coins, heads or tails. If you flip 3 fair coins, what are the relative frequencies of 3 heads; 2 heads and 1 tail; 1 head and 2 tails; and 3 tails

[AussieKenDoll]

Each proton splits the signal by ± 1/2. Consider this somewhat analogous to flipping coins, heads or tails. If you flip 3 fair coins, what are the relative frequencies of 3 heads; 2 heads and 1 tail; 1 head and 2 tails; and 3 tails

isn't it that 1:3:3:1 proportional to the concentration of the molecule's protons in each distinct chemical environments?

[sjb]

If you mean, for instance electronic environments, then yes. But for instance this is the splitting you'd see for the methylene in methyl ethyl ketone despite there only being two protons. I think you may be confusing to some degree splitting due to coupling and shifts of atoms in general.

[Babcock_Hall]

@OP,

I agree that the intensities provide the relative populations, and it may be applicable to another question that you had about coupling a month or two ago.

[phth]

see pascals triangle: a probability density pyramid. https://www.google.com/search?q=pascals+triangle&tbm=isch&chips=q:pascals+triangle,g_1:binomial+coefficient:Jebouxelg_w%3D&rlz=1C1CHBF_enUS901US901&hl=en&sa=X&ved=2ahUKEwinxr3Vh4LrAhWMnJ4KHXsVBlAQ4lYoCXoECAEQJw&biw=1903&bih=969