Aparticle is described by the wave function icircumlx

Question

A particle is described by the wave function

Ψ(x) ={ Axe^-ax, x>0

Ψ(x) ={ 0, x≤0

where A and a are constants.

(a.) Sketch the wave function.

(b.) Use the normalization condition to determine the constant A.

(c.) Find the most probable position of the particle.

(d.) Calculate the average value of the position of the particle.