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.
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).
we compute it by using their differences
The joint probability function for two variables is a probability function whose domain is a subset of two dimensional space. The joint probability function for discrete random variables X and Y is given aspr(x, y) = pr(X = x and Y = y). If X and Y are independent random variables then this will equal pr(X =x)*pr(Y = y).For continuous variables, the joint funtion is defined analogously:f(x, y) = pr(X < x and Y < y).
The joint probability function for two variables is a probability function whose domain is a subset of two dimensional space. The joint probability function for discrete random variables X and Y is given aspr(x, y) = pr(X = x and Y = y). If X and Y are independent random variables then this will equal pr(X =x)*pr(Y = y).For continuous variables, the joint funtion is defined analogously:f(x, y) = pr(X < x and Y < y).
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.
If f(x, y) is the joint probability distribution function of two random variables, X and Y, then the sum (or integral) of f(x, y) over all possible values of y is the marginal probability function of x. The definition can be extended analogously to joint and marginal distribution functions of more than 2 variables.
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.
A probability density function can be plotted for a single random variable.
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.
The probability is 1. The letters in the word mathematics are all constants, not variables!
The probability mass function is used to characterize the distribution of discrete random variables, while the probability density function is used to characterize the distribution of absolutely continuous random variables. You might want to read more about this at www.statlect.com/prbdst1.htm (see the link below or on the right)