Consider the random variable X with probability mass function P_{X}(k)=\left\{\begin{array}{cc} \alpha(3 k+5) & \text { for } k=0,1,2,3 \\ 0 & \text { otherwise } \end{array}\right. ) Calculate the value of a. ) Calculate the mean of X. ) Calculate the variance of X. =) Calculate P[X < 2].

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