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    Distribution Function of a Random Variable

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    A random variable X follows a distribution with probability density function

    (f_x)(x) = kx(1 - x), 0 < x < 1.

    (i) Determine the value of k.

    (ii) Find the probability P(0.4 <= x < 1)

    (iii) Find the value of a such that the cumulative density function F(a) = 0.6

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    Solution Summary

    The solution provides step by step method for calculating the distribution function of a random variable. Formula for the calculation and Interpretations of the results are also included.