Mathematics Homework Help

1. Consider a population of 8 units (y1, …, y8) = (15, 34, 35, 36, 11, 17, 36, 15). Sup- pose you take a simple random sample of size 3 with replacement.
   1. List all possible values of the sample total T.
   2. Find the sampling distribution of the sample total T .
   3. Let zi = 1 if unit i is selected into the sample and zi = 0 otherwise. Calculate the correlation of zi,zj.
   4. Recalculate the sampling distribution of T when sampling without replace- ment.
   5. Recalculate the correlation of zi , zj when sampling without replacement.
   6. Calculate mean and variance of the sample total T for both sampling withand without replacement distributions.

HI, I need someone to deal with this question 1, and also, I will provide some useful R code. thx