Hi.

I am struggling with Q1.21 for the first tutorial. I can do part (a) but I cannot understand how to do (b)

1.21 Suppose that deaths are uniformly distributed between consecutive integer ages. This problem sets out to show, step by step, that Tx−Kx then has exactly a uniform distribution on the interval (0,1).

\(f_x\) denotes the pdf of \(T_x\)

Show that for \(1\leq t < 2\) , \(f_x(t)\)= \(_tp_x\) \(q_{x+1}\)

Intuitively it makes a lot of sense. However, is there a way we could prove it? (if necessary)