<P> The mean of a probability distribution is the long - run arithmetic average value of a random variable having that distribution . In this context , it is also known as the expected value . For a discrete probability distribution , the mean is given by ∑ x P ( x ) ( \ displaystyle \ textstyle \ sum xP ( x ) ) , where the sum is taken over all possible values of the random variable and P ( x ) ( \ displaystyle P ( x ) ) is the probability mass function . For a continuous distribution , the mean is ∫ − ∞ ∞ x f ( x ) d x ( \ displaystyle \ textstyle \ int _ ( - \ infty ) ^ ( \ infty ) xf ( x ) \ , dx ) , where f ( x ) ( \ displaystyle f ( x ) ) is the probability density function . In all cases , including those in which the distribution is neither discrete nor continuous , the mean is the Lebesgue integral of the random variable with respect to its probability measure . The mean need not exist or be finite ; for some probability distributions the mean is infinite ( + ∞ or − ∞ ) , while others have no mean . </P>
<P> The mean of a probability distribution is the long - run arithmetic average value of a random variable having that distribution . In this context , it is also known as the expected value . For a discrete probability distribution , the mean is given by ∑ x P ( x ) ( \ displaystyle \ textstyle \ sum xP ( x ) ) , where the sum is taken over all possible values of the random variable and P ( x ) ( \ displaystyle P ( x ) ) is the probability mass function . For a continuous distribution , the mean is ∫ − ∞ ∞ x f ( x ) d x ( \ displaystyle \ textstyle \ int _ ( - \ infty ) ^ ( \ infty ) xf ( x ) \ , dx ) , where f ( x ) ( \ displaystyle f ( x ) ) is the probability density function . In all cases , including those in which the distribution is neither discrete nor continuous , the mean is the Lebesgue integral of the random variable with respect to its probability measure . The mean need not exist or be finite ; for some probability distributions the mean is infinite ( + ∞ or − ∞ ) , while others have no mean . </P>
what does the mean of probability distribution tell us
what does the mean of probability distribution tell us
the long - run arithmetic average value of a random variable having that distribution
the long - run arithmetic average value of a random variable having that distribution