The median of a continuous random variable with pdf f(x) is a real number m such that: ·m *** f(x)dx 91 [ f(x)dx Similarly, the first and third quartiles of a continuous random variable with pdf f(x) are real numbers 91, 93 such that - = 1 1 2 93 [ f(x) dx = 314 1+ax Let f(x) = ¹+ for −1≤ x ≤ 1 and f(x) = 0 otherwise, where -1 ≤ a ≤ 1. Show that f is a density, and find the corresponding cdf. Find the quartiles and the median of the distribution in terms of a.

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