Question

The law of large numbers states that as the number of observations drawn at random from a population with mean ? increases, the mean x-bar of the observed values:

a)tends to get closer and closer to the population mean ?
b) gets smaller and smaller
c) fluctuates steadily between 1 standard deviation above and 1 standard deviation below the mean
d) gets larger and larger.

Answer 1

Answer: a)tends to get closer and closer to the population mean ?

Explanation :

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and will tend to become closer to the expected value as more trials are performed.

Similarlly for population mean 'The law of large numbers states that an observed sample average from a large sample will be close to the true population average and that it will get closer the larger the sample'.

Hence In our case of problem The law of large numbers states that as the number of observations drawn at random from a population with mean ? increases, the mean x-bar of the observed values: a)tends to get closer and closer to the population mean ?.

All other option are not correct because number of observations increases mean x-bar of the observed values will not be smaller or larger and It will not fluctuate also.