Question

In a solar-panel factory, there are four labourers working Independently. Every weekday, each of the labourers assembles one panel after another, from start to finish, alone. In a simple model, assume that the average daily output of each person is an unknown constant: vi, v2. vs. and v. where vy E R ls the number of panels manufactured (decimals would represent Incomplete panelo). The jth person's output on the ith day can be modelled as random variable Hy with mean vy and standard deviation ơ, where ơ E R+, n this question we wish to estimate the four constants vy Because of the inefficient way that this factory organizes its inventory (a complicated system of sheives of palets),it's measure each employee's output. In fact, there's time to make only one (1) measurement of any kind at as the foreperson of the factory, measurement is perfectly accurate (noiseless). you may choose which person or group of persons to measure the output of each day. Each (a) (4 marks) For five upcoming weekdays, you decide on the following plan: Monday: Measure Mi HH12+ H3 . Tuesday: Measure M2-H21 H22 + H24 . Wednesday: Measure Ms HH33+Hs4 Thursday: Measure M4-H42+ H43+H44 Friday: Measure Ms Hs2+Hs Hs How precisely can you estimate vi using this plan? Specifically, describe the standard error ot Viin terms ot o, showing your work (b) (4 marks) In contrast, how precisely can you estimate vi by measuring just one labourer's daily output at a time, as follows: Monday: Measure MiHu Tuesday: Measure M2 2z2 Wednesday: Measure Ms-H3 . Thursday: Measure M4- H4 Friday: Measure Ms-Hs Show your work as always. (c) (2 marks) Given this question's ultimate objective of estimating all four constants v, do you prefer the experimental plan in (a) or (b)?

Answer 1