Different Kinds OF Speed (Most Probable Average and Root Mean Square) || Their Definition and Derivation form Maxwell Equation

Most probable speed, average speed and RMS speed are related as -

Most probable velocity, average velocity and root mean square velocity are related as

The ratio of average speed, most probable speed and root mean square speed of a gas sample will be

Respresent the relative values of most probable speed, average speed and root mean square speed on Maxwell's distribution curve for speeds.

What is the relation between average speed and root mean square speed for a gas ?

Define most probable speed, average speed and root mean square speed of a gas. How are they related to each other ?