The effect of Proportional Editing in Random mode is not as strong as I expected. How can I make it more intense? In this video ("Blender Beginner Tutorial - Part 4: Material Nodes", around minute 34) the author uses the "Proportional editing" mode and chooses the falloff type to be "Random".

I tried to do the same but it doesn't give the same wavy shape. I think the randomness effect isn't that great in my case but I don't know why. 



I tried to press W and then "Subdivide Smooth" to add more segments to the shape but I still don't achieve a great effect. 

Any ideas?
After having initiated the G ("move") action, scroll up the mouse wheel ( wheel) to enlarge the area of influence of the proportional edit.

While scrolling (up or down) you'll see a circle representing roughly to what spatial extent the other vertices will be affected. Make sure it is large enough to encompass several of the other vertices.

Then just keep moving the selected vertex to see the effect. (As Ashutosh Budhdeo noted, you may want to use Z during the "move" action to constrain the movement to the vertical axis).