Wald’s identity is one lemma used to find this quantity for a series of IID random variables that only requires knowledge of the random variable and the stopping time. Finding this quantity using the tower rule first involves obtaining that same quantity conditioned on a random (15[1])variable. This quantity remains the same for present and future observations in filtrations that Jean Ville named after the martingale betting (15[1])system. (15[1])Calculating this quantity for “e to the t X” yields the (*) moment-generating (10[3])function. This (10[1])quantity is almost surely (10[1])obtained after infinite trials according to the strong law of large (10[2]-5[1])numbers. For a random variable (10[1])X, this quantity of (10[1]-5[1])X-squared minus the square of this quantity of X equals its (-5[1])variance. For 10 points, name this weighted average of all possible (10[3])outcomes. (10[5]0[2])■END■