For the levelling network shown in Figure $2,$ estimate the most probable elevations for $x,Y,$ and $Z.$ The observed values and line lengths are given in Table $2,$ so apply appropriate weights in the solution. Estimate the residuals, adjust the observations, and compute the a$-$posteriori variance factor. Also, compute the standard deviations of the estimated elevations, and the standard deviations of the adjusted elevation differences.

Figure $2.$ Levelling network

Table $2.$ Observations and line lengths

$\backslash$table$[[$Line$,$Length $($miles$),h[ft]$