Sample Spaces of Distributions 4 points possible (graded) Recall that a sample space of a random variable X is a set that contains all possible outcomes of X. Note that the sample space of X is not unique. For example, if X N Ber (p), then both {0, 1} and R can serve as a sample space. However, in general, we associate a random variable with its smallest possible sample space (which would be {0, 1} if X N Ber (p)). Find the smallest sample space for each of the following random variables. X1 ~ Poiss (A), a Poisson random variable with parameter A: 0 {0,1} 0 {x E Z : a: 2 0} O [0, 00) O (00, co) X2 N N (0, l), a standard Gaussian (or normal) random variable with mean 0 and variance 1: 0 {0,1} 0 {as E Z : :r: 2 0} O [0, oo) 0 (00, 00) X3 N exp (A), an exponential random variable with parameter /\\ > 0: