A constant random variable is a random variable 
for which 
with probability 1 for some constant 
. Its statistical distribution
is a point mass at 
, its expectation value
is 
,
and its variance is zero.
Constant Random Variable
See also
Expectation Value, Random Variable, VarianceExplore with Wolfram|Alpha
References
Grimmett, G. and Stirzaker, D. Probability and Random Processes, 3rd ed. Oxford, England: Oxford University Press, 2001.Cite this as:
Weisstein, Eric W. "Constant Random Variable." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConstantRandomVariable.html