Mean of a probability distribution Mean

the mean of probability distribution long-run arithmetic average value of random variable having distribution. in context, known expected value. discrete probability distribution, mean given




∑
x
p
(
x
)



{\displaystyle \textstyle \sum xp(x)}

, sum taken on possible values of random variable ,



p
(
x
)


{\displaystyle p(x)}

probability mass function. continuous distribution,the mean





∫

−
∞


∞


x
f
(
x
)

d
x



{\displaystyle \textstyle \int _{-\infty }^{\infty }xf(x)\,dx}

,



f
(
x
)


{\displaystyle f(x)}

probability density function. in cases, including in distribution neither discrete nor continuous, mean lebesgue integral of random variable respect probability measure. mean need not exist or finite; probability distributions mean infinite (+∞ or −∞), while others have no mean.