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Statistics and probability

Course: Statistics and probability>Unit 10

Lesson 1: What is a sampling distribution?

Introduction to sampling distributions

AP.STATS:
UNC‑3 (EU)
,
UNC‑3.H (LO)
,
UNC‑3.H.1 (EK)
Introduction to sampling distributions.

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• How come the balls are repeated in a pairing when there is only one of that number of balls?
Like, in the population there is only 1 of 1 ball. How come there is a pair (1,1) when there's only 1 of 1 ball??
• Notice Sal said the sampling is done with replacement. This means during the process of sampling, once the first ball is picked from the population it is replaced back into the population before the second ball is picked.
This helps make the sampling values independent of each other, that is, one sampling outcome does not influence another sampling outcome.
• What kind of distribution is it then, if not binomial?
• As the n in binomial approaches infinity, the model will become more and more normal. You will learn in Chapter 22 about degrees of freedom.
• Python visualization.
``import matplotlib.pyplot as pltimport itertools as itans =list(it.combinations_with_replacement(range(20),2))ansr = []for i in ans:    ansr.append(i[::-1])res = list(set(ans+ansr))for i,j in enumerate(res):    res[i] = sum(j)/len(j)fig = plt.hist(res,rwidth = 0.6,bins = len(ans))fig = plt.grid('off')plt.show()``
• What does parameter actually mean in statistics?
• A parameter is a measurement of a characteristic of a population such as mean, standard deviation, proportion, etc.

This is in contrast with a statistic, which measures a characteristic of a sample rather than a population. Statistics are frequently used to estimate parameters.

Have a blessed, wonderful day!
• Around , when he gets the sample mean '1.5' out of the balls '1' and '2', how did he get that mean? I don't understand. Also same question for time stamp , how did he get all of those decimal answers??
• Mean = all points added up divided by number of points
Sample Mean = (1+2)/2 = 1.5
• Why is a sample of {2, 1} considered different from {1, 2}?
• Actually I think I get it now; it's so that all the possible outcomes (means) are equally likely, so that you can put the absolute frequency of a mean over the total # of outcomes to get the relative frequency.
• In general, what estimates better the mean? One only big sample or several smaller samples?
• I am confused about the name - what does "Sampling" mean in "Sampling distribution of the sample means"? And why is sample/sampling mentioned twice "Sampling" and "sample" in sample means? Is it not enough to say "Distribution of the sample means"?