Question

Sampling Distribution. We will be using some of your knowledge of statistics this semester, so you may need to use the resources you were provided in other class(es) and review a few concepts. First, review the meaning of the term "sampling distribution," as defined in your statistics course(s).

After looking it up in your statistics sources, read the following:

http://onlinestatbook.com/2/sampling_distributions/intro_samp_dist.html

Now work on the following problem:

I have a random variable that represents the flip of a fair coin. If the outcome of the flip is Heads, the random variable takes on the value 1, and if it is Tails, it takes on the value 0. I am taking samples of size n=4, so a sample might look like {0, 1, 0, 0}. For this particular sample, the sample min is 0, the sample mean is 1/4, and the sample max is 1. Give the sampling distributions for the sample mean, the sample min, and the sample max. Use as many or as few of the lines of the tables below as you need.

Sampling Distribution of the sample min:

Outcome of the sample min	Probability

Sampling Distribution of the sample mean:

Outcome of the sample mean	Probability

Sampling Distribution of the sample max:

Outcome of the sample max	Probability

Answer 1

OUTCOMES OF THE SAMPLE - MIN	PROBABILITY
0	15/16
1	1/16

OUTCOMES OF THE SAMPLE -MAX	PROBABILITY
0	1/16
1	15/16

OUTCOMES OF THE SAMPLE - MEAN	PROBABILITY
0	1/16
1/4	4/16
1/2	6/16
3/4	4/16
1	1/16

denominator is 16 in each case is because the total no of outcome is 16.

JUSTIFICATION: In the sample space, there is two options(0,1) for each 4 place. So, total no of outcome becomes 2*2*2*2=16.

If you need more detailed explanation, let me know in the comment section, I will surely help you. and if it helps, dont forget to upvote. Thank you.