Hi, I am new to MLC and the first thing I noticed is the numerous notations that look rather foreign to me. I am feeling extremly frustrated and I realized that I can't go any further before straightening these things out.

[note: I am using _ to represent subscripts]

1) t_p_x

Is this a function of x? a function of t? or a function of both? It seems to me that neither of the above makes sense.

If it's a function of x, why am I seeing formulas for (d/dt) t_p_x?

If it's a function of t, why am I seeing formulas for (d/dx) t_p_x?

If it's a function of both x and t, shouldn't (d/dx) t_p_x and (d/dt) t_p_x bepartialderivatives?

2) In the formula for deferred mortality probability t|u_q_x, I am seeing the survival function in the form s(x+t+u), is this a function of three variables x,t, and u, i.e. f(x,t,u)=s(x+t+u) for some function f? Or are some of the variables "fixed"?

3) (Force of mortality)

I am OK with µ(x), but once again I am confused about something like µ(x+t).

Consider the formula µ(x+t)=s'(x+t)/s(x+t)

a) I don't understand the meaning of the notation µ(x+t). Is µ(x+t) a function of both x and t?

b) For s'(x+t), is it differentiating with respect to x? to t? to z=x+t?

c) For s'(x+t), is it apartialderivative?

4) (Force of mortality)

[note: once again I'm using _ to indicate subscripts]

One of the formulas says that µ_X (x+t) = µ_T(x) (t)

a) What is the meaning of putting subscripts X and T(x) to the right of µ?

b) What is the difference between µ(x+t) and µ_X (x+t)?

Please help me out. Any help would be greatly appreciated!