Question

A random sample from a population is given below. 35, 45, 40, 42, 39, 55 and 63. Obtain the moment estimator of the population mean.

Hint:

The moment estimator of the population mean is simply the sample mean, which provides an unbiased estimate of the true population mean.

Answer 1

Step 1: Moment estimator of the mean.
The moment estimator for the population mean is the sample mean, which is calculated as the sum of all observations divided by the number of observations.
Step 2: Calculate the sample mean.
The data provided is: 35, 45, 40, 42, 39, 55, 63. The sample mean is: \[ \bar{x} = \frac{35 + 45 + 40 + 42 + 39 + 55 + 63}{7} = \frac{319}{7} = 45.57 \]
Step 3: Conclusion.
The moment estimator of the population mean is the sample mean, which is approximately 45.57.