# sampling distribution

1. Construct the sampling distribution for the outcomes of an ordinary 6-sided die.

Solution:

There are 6 possible outcomes in rolling an ordinary 6-sided die.

Since it is just an ‘ordinary’ die, it is safe to assume that each outcome is equally likely to occur. Since the total probability is 1, each outcome has a probability of 1/6 to occur.

Let X = outcome of rolling an ordinary 6-sided die.

The distribution of X would be

P(X = 1) = 1/6

P(X = 2) = 1/6

P(X = 3) = 1/6

P(X = 4) = 1/6

P(X =5) = 1/6

P(X = 6) = 1/6

The sampling distribution of the outcome can also be expressed as

P(X = x) =1/6, for x = 1,2,3,…,6

P(X = x) = 0, otherwise.

1. What is the mean, variance, and standard deviation of this sampling distribution.

The mean of X is equal to

= 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6) = 3.5.

The variance is equal to

= 35/12

≈ 2.9167 [4 decimal places]

The standard deviation is equal to the square root of the variance.

1.7078 [4 decimal places]