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The answer depends on whether or not the two variables are independent.
It does not have to. It is simply a study where two variables have a joint probability density function. There is no requirement for both variables to be dependent - one may be dependent on the other (which is independent).
There is no fixed value: it depends on the consequences of making the wrong decision. For example, when the consequences are very serious then a very high probability is required. A popular level is a probability value of 95% but that number has no particular significance.There is no fixed value: it depends on the consequences of making the wrong decision. For example, when the consequences are very serious then a very high probability is required. A popular level is a probability value of 95% but that number has no particular significance.There is no fixed value: it depends on the consequences of making the wrong decision. For example, when the consequences are very serious then a very high probability is required. A popular level is a probability value of 95% but that number has no particular significance.There is no fixed value: it depends on the consequences of making the wrong decision. For example, when the consequences are very serious then a very high probability is required. A popular level is a probability value of 95% but that number has no particular significance.
Yes- the highest probability value is the mode. Let me clarify this answer: For a probability mass function for a discrete variables, the mode is the value with the highest probability as shown on the y axis. For a probability density function for continuous variables, the mode is the value with the highest probability density as shown on the y-axis.
There is no such thing as definite variable in mathematics. Some of the variables in mathematics are independent and dependent variables. More variables are usually found in probability textbooks.