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Distributionshard
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Consider a random variable XXX whose probability density function is f(x)=k(1−x2)f(x) = k(1 - x^2)f(x)=k(1−x2) for x∈[0,1]x \in [0, 1]x∈[0,1]. To satisfy the requirements of a valid PDF, what is the value of the constant kkk and the resulting skewness of XXX?