X is a continuous random variable with probability density function of f(x) = k(6x-3x^2), 0<=x<=2 a. Show that k = 1/4 makes f(x) a valid probability density function. b. using k = 1/4, find the mean of X. c. Using k=1/4, find the cumulative distribution function F(x) of X. (Include the appropriate domain.)

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