Let \alpha be an unknown constant and X a discrete random variable with the following PMF:
$P_X[x_i] = egin{cases} 2\alpha, & x_i = -1 \\ 2\alpha, & x_i = 0 \\ 3\alpha, & x_i = 1 \\ \alpha, & x_i = 2 \\ 0, & \text{otherwise} \end{cases}$
(a) (4 points) Find the value of \alpha that makes $P_X[x_i]$ a valid PMF.
(b) (2 points) Using your value of \alpha above, compute the probability that $X < 1$.
(c) (2 points) Using your value of \alpha above, compute the probability that $|X| = 1$.
(d) (4 points) Consider 6 independent draws of X. What is the probability that X = 0
on exactly 2 of the draws?
