JProve $T_1$ is finite if there exists bijection from $T_1$ to another finite set $T_2$

Assuming $ T_1$ is non empty. Prove $ T_1$ is finite if there exists bijection from $ T_1$ to another finite set $ T_2$

Now we have $ h : J_m \to T_1$

Assume another finite set $ T_2$ , so we have $ h_1 : J_m \to T_2$ .

Since both $ h_1$ and $ h_2$ are bijections. so is $ h_1 \circ h^{-1}$

$ J_m$ = $ {1,2,3,…,m$ }

Conversely, similar idea to that of this. But is this even correct ?

Thanks

$T_1, … , T_n$ time of life of instruments with geometric distribution of parameter p independent

$ T_1, … , T_n$ time of life of instruments with geometric distribution of parameter p independents. I define S as the first n instants of failure and U as the last n instant of failure. I want to find the law of S and the density of U.

This is what I did so far:

To find the law of S I start by calculating: $ $ \mathbb{P}(S = k) = \mathbb{P}(S \geq k) – \mathbb{P}(S \geq k + 1) $ $ $ $ \mathbb{P}(S = k) = \mathbb{P}(S < k+1) – \mathbb{P}(S < k)$ $ But here I am stuck on what I should do because I still do not know the distribution.

I do the same reasoning with U as follows: $ $ \mathbb{U}(S = k) = \mathbb{U}(U \leq k) – \mathbb{U}(S \leq k + 1) $ $ But I still get nowhere.

Any suggestions?