expectation expectation it is often useful to consider different kinds of numerical characteristics of random variable one such quantity is the expectationwhich measures the "averagevalue of the distribution the expectation (or expected value or meanof random variable with pdf denoted by ex or [ (and sometimes )is defined by discrete caser (xex (xdx continuous case if is random variablethen function of xsuch as or sin( )is again random variable moreoverthe expected value of function of is simply weighted average of the possible values that this function can take that isfor any real function discrete caser (xf (xeh(xh(xf (xdx continuous casevariance standard deviation provided that the sum or integral are well-defined the variance of random variable xdenoted by var (and sometimes )is defined by var ( [ ]) ex (ex) the square root of the variance is called the standard deviation table lists the expectations and variances for some well-known distributions both variance and standard deviation measure the spread or dispersion of the distribution notehoweverthat the standard deviation measures the dispersion in the same units as the random variableunlike the variancewhich uses squared units table expectations and variances for some well-known distributions dist ex var bin(npnp np( pgeom( poi(lu[abexp(ltn dist ex var gamma(ala (us beta(aba + ab ( + ) ( + +ba+ ( ) weib(alg( /aal ( /ag( /aa al ( - (mnn - ( ( + - ( - ) ( - ( ( we only use brackets in an expectation if it is unclear with respect to which random variable the expectation is taken