[100] Suppose you roll two twenty-five-sided dice. Let X1, X2 the outcomes of the rolls of these two fair dice which can be viewed as a random sample of size 2 from a uniform distribution on integers.

List all possible samples and calculate the value of the sample mean (X) and variance (s^2) for each sample?

Here is the full question part:

[100] Suppose you roll two twenty-five-sided dice. Let X1, X2 the outcomes of the rolls of these two fair dice which can be viewed as a random sample of size 2 from a uniform distribution on integers.

List all possible samples and calculate the value of the sample mean (X) and variance (s^2) for each sample?

a) What is the population from which these random samples are drawn?

Find the mean and variance of this population

b) List all possible samples and calculate the value of the sample mean (X) and variance (s^2) for each sample?

a)  mean  = 13

     variance of this population = 52

b)  a table is make in a document file attach below show all the possible samples with their corresponding calculation of the sample mean (X) and their corresponding variance for each sample

Step-by-step explanation:

a)

A random sample of 2 is collected from : P (X = x)  = ;

where x = 1,2,3 ... , 25 = 0 otherwise

 =

= 13

= 13 × 17

= 13 × 4

= 52

b) The document below clearly depicts the lists of  all the possible samples with their calculated value of the sample mean (X) and variance  for each sample.

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.