WebFeb 5, 2024 · Mathematically, the standard deviation of a set of position data is determined by (6.4.13) σ x = < x 2 > − < x > 2 i.e., the difference between the expectation value of the square of x and the expectation value of x squared. Thus, to find the uncertainty in position, we need the expectation value of x2: WebExpected value of an exponential random variable Let X be a continuous random variable with an exponential density function with parameter k. Integrating by parts with u = kx and dv = e−kxdx so that du = kdx and v =−1 ke −kx, we find E(X) = Z∞ −∞ xf(x)dx = Z∞ 0 kxe−kxdx = lim r→infty [−xe−kx− k 1 e−kx] r 0 = 1 k 2
Expected value of an exponential random variable
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