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stukbv
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What is the difference between disjoint and independent events, how will the 2 affect calculations involving them?
sfs01 said:Disjoint events are mutually exclusive, which is a strong form of statistical dependence (so if you know event A occurred you know that B definitely did not occur and vice versa), meaning
[tex]P(A\cap B) = 0[/tex]
[tex]P(A\cap B) = P(A) P(B)[/tex]
Which events are meant to be both independent and disjoint in this case? The only way I can see that two events can ever be both independent and disjoint is if one of them has probability zero.SW VandeCarr said:Well, tossing a fair coin leads to series of events that are both independent and disjoint. I wouldn't say that fair coin tosses are in any way dependent on each other.
In the usual sense, statistically independent events are not either/or outcomes. So for the tossing of a fair coin, the probability of H or T is exactly 1,and the third term is zero, not P= 1/4. However, as you say, if P(A) and P(B) are the probabilities of random independent events which are not mutually exclusive, then the sum of the probabilities is P(A)+P(B)-P(A)P(B); that is, the probability of A or B, less the probability of A and B.
I was just concerned that your description of disjoint events as representing a strong form of dependence might be confusing to some.
stukbv said:So when we have evens and we say the probability of their union is equal to their sum, does this mean they are independent or disjoint ?
Disjoint or independent are terms used to describe two or more variables that have no relationship or influence on each other. In other words, changes in one variable do not affect the other variable.
To determine if two variables are disjoint or independent, a statistical analysis such as a correlation or regression can be performed. If the result is close to 0 or the p-value is above the significance level, it indicates that the variables are disjoint or independent.
Identifying disjoint or independent variables is crucial in research because it allows for accurate and unbiased analysis. It also helps to avoid drawing incorrect conclusions or making false associations between variables.
Yes, it is possible for two variables to be disjoint or independent in one context or scenario, but related in another. This is why it is important to thoroughly analyze and understand the variables in a specific research study before drawing conclusions.
To control for confounding variables in a study of disjoint or independent variables, researchers can use experimental design techniques such as randomization or matching. These methods help to ensure that any observed relationship between variables is not due to the influence of a third variable.