For 10 points, identify these "variables" that assign a numerical value to events in a sample space and are used to calculate probabilities.
A function that defines these things can be found by taking the Radon-Nykodym derivative of the induced measure with respect to a counting or a Lebesgue measure. The properties of these things can be defined by taking the first and second derivatives of the moment-generating function and evaluating them at zero. The joint CDF for these things is given by the convolution of each one's CDF. For one of these denoted capital X, the expected value of X squared minus the expected value of X, all squared is equal to the variance. For 10 points, identify these "variables" that assign a numerical value to events in a sample space and are used to calculate probabilities.
A function that defines these things can be found by taking the Radon-Nykodym derivative of the induced measure with respect to a counting or a Lebesgue measure.
random variables [or r.v.\'s; or stochastic variables; or probability distributions; prompt on measure spaces]