Sample Statistics - Revision history

Admin: /* Experimental Probability */

2024-03-19T06:11:58Z

Experimental Probability

← Older revision		Revision as of 06:11, 19 March 2024
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	The '''complement''' of event A is all outcomes that does not belong to A.		The '''complement''' of event A is all outcomes that does not belong to A.

	== Terminology ==		== Misc. Terminology ==
	The two events are '''mutually disjoint''' if their ''intersection'' is the null set.		The two events are '''mutually disjoint''' if their ''intersection'' is the null set.

			When we select observations randomly from a population, if the observation can be selected again, the selection is done '''with replacement'''. Otherwise, it is '''without replacement'''.

	= Probability =		= Probability =
	The '''probability''' of an event is a number representing how likely an outcome belongs to the event. It is pretty intuitive so I'm going to skip on explaining it.		The '''probability''' of an event is a number representing how likely an outcome belongs to the event. It is pretty intuitive so I'm going to skip on explaining it.

	=== Classic Probability ===		== Classic Probability ==
	'''Logic based''' (or '''classic''') probability assumes all possible events are equally likely based on a logical/natural assumption. We assume we know all possible otucomes in advance, and the probability is calculated by		'''Logic based''' (or '''classic''') probability assumes all possible events are equally likely based on a logical/natural assumption. We assume we know all possible otucomes in advance, and the probability is calculated by

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	As the number of samples increased, so do the accuracy of this sample probability.		As the number of samples increased, so do the accuracy of this sample probability.

			== Fundamental Rules ==
			There are serveral fundamental rules of probability that I'm not gonna elaborate on since they are pretty intuitive.

			# All probability add up to 1
			# Probability is between 0 and 1
			# P(A) = 1 - P(A<sup>C</sup>)
			# <math>P(A \cup B) = P(A) + P(B) - P(A \cap B)</math>

			== Conditional Probability ==
			We are interested in the probability of an event given that another event has been observed. This is the '''conditional probability''' of ''A given B'':

			<math>P(A\|B) = \frac{P(A \cap B)}{P(B)}</math>

			Doing some quick substitutions, we have '''Bayes' Theorem''', giving us P(A\|B) if we have P(B\|A) It's literally just substitution.

			<math>P(A\|B) = \frac{P(B\|A) P(A)}{P(B\|A) P(A) + P(B\|A^C) P(A^C)}</math>

Admin: /* Experiment */

2024-03-19T05:53:29Z

Experiment

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 A '''population parameter''' is the value of a statistic based on population data. This is almost always not measurable. A '''sample statistic''' is the value of a statistic based on sample data. We use sample statistics to estimate population parameters.
-= Experiment =
+= Experiment and Events =
-An '''experiment''' is a process that results in a random outcome
+An '''experiment''' is a process that results in a random outcome that cannot be known in advance with certainty. We are interested in a particular subset of outcomes: an '''event'''.

Admin: Admin moved page Probability to Sample Statistics

2024-03-19T05:43:29Z

Admin moved page Probability to Sample Statistics

← Older revision		Revision as of 05:43, 19 March 2024
(No difference)

Rice: Created page with "Category:Sample Statistics A '''population parameter''' is the value of a statistic based on population data. This is almost always not measurable. A '''sample statistic''' is the value of a statistic based on sample data. We use sample statistics to estimate population parameters. = Experiment = An '''experiment''' is a process that results in a random outcome"

2024-03-19T05:42:23Z

Created page with "Category:Sample Statistics A '''population parameter''' is the value of a statistic based on population data. This is almost always not measurable. A '''sample statistic''' is the value of a statistic based on sample data. We use sample statistics to estimate population parameters. = Experiment = An '''experiment''' is a process that results in a random outcome"

New page

[[Category:Sample Statistics]]
A '''population parameter''' is the value of a statistic based on population data. This is almost always not measurable. A '''sample statistic''' is the value of a statistic based on sample data. We use sample statistics to estimate population parameters.

= Experiment =
An '''experiment''' is a process that results in a random outcome