= Solution
Let $R_i=\{j:x_j\geq x_i\}$ be the <risk set> at an observed event time $x_i$. In the <Cox proportional-hazards model>, conditional on one member of this set failing then and on the preceding history, the probability that it is individual $i$ is
$$
\frac{e^{\beta z_i}h_0(x_i)}{\sum_{j\in R_i}e^{\beta z_j}h_0(x_i)}
=\frac{e^{\beta z_i}}{\sum_{j\in R_i}e^{\beta z_j}}.
$$
The <baseline hazard> cancels. Multiplying these conditional contributions gives the <Cox partial likelihood>
$$
\boxed{L_p(\beta)=\prod_{i:v_i=1}\frac{e^{\beta z_i}}{\sum_{j:x_j\geq x_i}e^{\beta z_j}}.}
$$
The no-ties assumption avoids the need for a tied-event approximation. This construction assumes <independent censoring> conditional on the modelled covariates. The printed phrase calling $z$ a scalar parameter is read as a scalar observed covariate $z_i$; $\beta$ is the unknown regression parameter.
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