What was pairwise independent and mutually independent events?
Mutually independent events are events where each event is independent from any collection of the other events. For example, If you toss a bunch of coins, the result of each one is independent from all the others. Pairwise independent events are groups of events where each pair of events is independent.
What does pairwise mean in statistics?
Pairwise comparisons are methods for analyzing multiple population means in pairs to determine whether they are significantly different from one another. As an example, many different statistical methods have been developed for determining if there exists a difference between population means.
Can 3 events be independent but not pairwise independent?
Consider two events A and B such that P{A ∩ B} = P{A}P{B}, i.e., they are de- pendent events. Now consider a third event C = ∅. So although every set of three events in this collection (there is only one set of three events) has the independence property, this collection is not pairwise independent.
What is the difference between independent and mutually independent?
The difference between mutually exclusive and independent events is: a mutually exclusive event can simply be defined as a situation when two events cannot occur at same time whereas independent event occurs when one event remains unaffected by the occurrence of the other event.
What is pairwise method?
Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some quantitative property, or whether or not the two entities are identical. In psychology literature, it is often referred to as paired comparison.
Are a B and C mutually independent?
Events A and B are dependent (P(A|B)≠P(A)×P(B) and P(B|A)≠P(A)×P(B)) and so events A, B and C are not mutually independent. Mutual Independence of three events For any three events A, B and C to be mutually independent the following two conditions must be met: P(A∩B∩C)=P(A)×P(B)×P(C)
What is the difference between mutual independence and pairwise independence?
Mutual independence: Every event is independent of any intersection of the other events. Pairwise independence: Any two events are independent.
What is meant by mutually independent?
A finite set of events is mutually independent if every event is independent of any intersection of the other events.
Are AI and AJ pairwise independent?
The events A1,A2,A3 are pairwise independent if, for all i = j, Ai is independent of Aj.
What is the difference between independent and dependent events?
Dependent events influence the probability of other events – or their probability of occurring is affected by other events. Independent events do not affect one another and do not increase or decrease the probability of another event happening.
Which is the best definition of pairwise independence?
Pairwise independence. Jump to navigation Jump to search. In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent.
How to calculate the number of independent pairwise comparisons?
The formula for the number of independent pairwise comparisons is k(k-1)/2, where k is the number of conditions. If we had three conditions, this would work out as 3(3-1)/2 = 3, and these pairwise comparisons would be Gap 1 vs .Gap 2, Gap 1 vs. Gap 3, and Gap 2 vs. Grp3. Notice that the reference is to “independent” pairwise comparisons.
Are there any random variables that are not pairwise independent?
Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables with finite variance are uncorrelated.
Can a pairwise independent event be mutually independent?
From what I gather, the events can be pairwise independent as long as P(A & B & C)equal the same probability. For mutually independence, it is true if they equal 1 over the total possibilities. Am I correct to say that?$\\endgroup$– o.oSep 28 ’15 at 0:39