28 The probability distribution associated with the outcome of rolling a balanced die has probability 1/6 attached to each integer, 11, 2.3 4.5.6). Consider the experiment of rolling a balanced die twice

a) Enumerate the 36 possible pairs of numbers, taking into account the order of rolling (eg (1,2), representing a 1 followed by a 2. is different fioin (2, 1)).

b) Treating these 36 pairs as equally likely. construct the sampling distribution for the sample mean of the two numbers rolled.

c) Construct a histogram of the sampling distribution in (b). What is its shape?

d) Calculate the mean of the sampling distribution in th), and show that it is identical to the mean of the population distribution.