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Random Variableshard
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A continuous random variable XXX has a probability density function f(x)=k(1−x3)f(x) = k(1 - x^3)f(x)=k(1−x3) for 0≤x≤10 \le x \le 10≤x≤1. If E[X]=12E[X] = \frac{1}{2}E[X]=21​, which of the following is true regarding the value of kkk and the existence of such a random variable?