I rarely have math questions I don\'t know how to do. I assist students in study
ID: 3182306 • Letter: I
Question
I rarely have math questions I don't know how to do. I assist students in studying (I'm not allowed to post the t*tor word on this site). This question I am not understanding what is bein asked. The problem states that x is a discrete random variable with values {1, 2, 3, 4, 5} and probabilities of {0.2, 0.3, 0.2, 0.2, 0.1}. We are to select 2 values of x at random and calculate the probability of the event. this is easy. For example, P(1, 1) = 0.2 x 0.2 = 0.04. Then we are to create a table of all possible values of 2 samples (1,1), (1,2), (1,3),....,(5,3), (5,4), (5,5) for a total of 25 samples of 2 and calculate the probabilities of all of those. Again, easy (just multiply the respective two probabilities).
Where I am lost is the problem asks to find the distribution of s^2 (sample varience). I expect this is asking us to create a table of all possible values of the sample varience using the sample size of 2. But then I don't know what to do with this? I already calculated the possible varience values for all 25 cases, and they are: 0, 0.125, 0.5, 1.125, and 2. But coming up with a table for the varience distribution, I don't know what to do. The idea of this problem is to show that the sample variences are an unbiased predictor of the population varience. But I have no idea how to go there?
Explanation / Answer
Calculate sample variance using your 25 samples of size 2.
We know sample variance is unbiased estimator of population variance.
Take sum of all these 25 sample variance and divide it by 25, the result gives the estimate of population variance.