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A population contains 10 units, labelled U1, U2, U3,.......U10. The value of a character Y under study, for Ui is Yi(1<=i<=10). In order to estimate the population mean, Y*, a sample of size 4 is drawn in the following manner:

  1. A simple random sample of size 2 is drawn without replacement from the units U2,U3,......U9; 2)The sample drawn in the first step is augmented by the units U1 and U10. Based on the above sample in the second part, suggest an unbiased estimator of Y* and obtain its variance.

The most basic question I want to ask here is not about the unbiased estimator, but how is Y related to U1,.....? 'Character under study for Yi' what does the phrase indicate?

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  • $\begingroup$ $Y$ is a random variable, which can be characterized as associating a number with each unit. $\endgroup$
    – whuber ♦
    Commented Jul 2, 2020 at 19:41
  • $\begingroup$ Based on the understanding, I developed from the link above. $U1,U2....$ can be considered as the tickets in the box and $Y1,Y2....$ are the values of the change in investment. right? $\endgroup$
    – Nisha
    Commented Jul 3, 2020 at 2:28
  • $\begingroup$ So, $U1,U2,....$ are the random variables that we will proceed with $\endgroup$
    – Nisha
    Commented Jul 3, 2020 at 2:29
  • $\begingroup$ The $U_i$ are the outcomes. The map $Y:U_i\to Y_i$ is a single random variable. $\endgroup$
    – whuber ♦
    Commented Jul 3, 2020 at 14:06

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