4 9. Let p(x) for x > 0 (and p(x) = 0 if x < 0). T(1+(2x)²) (a) Show that p is a probability density function. (b) If X is the associated random variable, find the median of X. (c) Show that the mean of X is infinite. This is strange: A finite amount of "mass" can be distributed along the positive number line in a way that the line does not balance at any point, but instead tips infinitely hard to the right at each location.

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