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Suppose that X is a random variable with probability density function given by: fx(x) = k(x' +2), 05x - 2; 0, otherwise. (Note that you must determine the value of the constant / in part 1 below and use it in all subsequent parts of this problem.)
1. Calculate the value of k so that fx is a valid probability density function.
2. Having found k, state the cumulative distribution function Fx. (Express your answer as a piecewise-defined function.)
3. Calculate the probability P[X & 1].
4. Calculate Ex, the expected value of X.
5. Calculate o?, the variance of X.
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