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2. (18 marks) Let X denote the amount of space occupied by an article placed in a 1-ft? packing container. The pdf of X
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2. (18 marks) Let X denote the amount of space occupied by an article placed in a 1-ft? packing container. The pdf of X is f(x) = { fix*(1 – 2) 0 < x < 1 otherwise (a) Find the value of k such that f(x) is a valid pdf. (b) Find the mean and variance of X. (c) Find the probability density function of Y = 1 - X. (4 marks) (8 marks) (6 marks)