From Wikipedia:

/.../ a particle's distribution function is a function of seven variables, $f ( x , y , z , t ; v_ x , v_y , v_ z )$, which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity $( v_x , v_y , v_z)$ near the place $( x , y , z )$ and time $( t )$.

Question:

We have $\frac{dx}{dt}=v_x(t)$, $\frac{dy}{dt}=v_y(t)$ and $\frac{dz}{dt}=v_z(t)$. Therefore the explicit form of $f$ is actually $$ f ( x(t) , y(t) , z(t) , t ; v_ x(t) , v_y(t) , v_ z(t) ) $$ Is this a correct interpretation?

From Wikipedia:

... a particle's distribution function is a function of seven variables, $f ( x , y , z , t ; v_ x , v_y , v_ z )$, which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity $( v_x , v_y , v_z)$ near the place $( x , y , z )$ and time $( t )$.

We have $\frac{dx}{dt}=v_x(t)$, $\frac{dy}{dt}=v_y(t)$ and $\frac{dz}{dt}=v_z(t)$. Therefore the explicit form of $f$ is actually $$ f ( x(t) , y(t) , z(t) , t ; v_ x(t) , v_y(t) , v_ z(t) ) $$ Is this a correct interpretation?