4. Use the following probability distribution to answer parts (a), (b), (c) and (d). Note that p(x) is 0 for any values of x other than 0, 3, 6 or 7.

x	0	2	5	6
p(x)	.3	.2	.4	.1

(a) Explain why p(x) is in fact a legitimate probability distribution.

(b) Determine the cdf F(x), making sure to specify the value of F(x) for all real number inputs, and sketch a graph of F(x) that shows the value of F(x) for any real number x.

(c) Calculate the expected value of X (the population mean of X).

(d) Calculate the population variance and standard deviation.