Question One (20 points): The probability distribution function (PDF) of a discrete random variable X is shown in Table 1. Answer the following questions:
(1) What is p, the probability for X to be -2? (3 PTS)
(2) What is the mean of X? (3 PTS)
(3) What is the median of X? (3 PTS)
(4) What is the mode of X? (3 PTS)
(5) What is the standard deviation of X? (3 PTS)
(6) Given the PDF of X, what is the mean (or expected value) of (X+2X²)? (5 PTS)
Table 1: The probability distribution function (PDF) of X
X | -4 | -2 | 0 | 2 | 4
P(x) | 0.1 | p = ? | 0.3 | 0.2 | 0.2