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Consider a discrete random variable X with the following probability function:

$\begin{array}{c|c} x & P( X = x ) \\ \hline -3 & \\ 0 & \\ 2 & \\ 4 & \\ \end{array}$

Answer the following questions, rounding your answers to two decimal places where appropriate.

(a) What is the expected value of $X$ ?

(b) What is the standard deviation of $X$ ?

(c) What is the expected value of $2X$ ?

(d) What is the standard deviation of $2X$ ?

(e) What is the expected value of $2X-3$ ?

(f) What is the standard deviation of $2X-3$ ?

(g) What is the expected value of $X^2$ ?

(h) Consider the random variable $Y = 10 + 6X$ . What is $P(Y \le )$ ?

You can earn partial credit on this problem.