A spinner marked off in seven ​equal-sized regions, numbered 1, 2, 3, 4, 5, 6, and 7​, is spun twice. Let the random variable X be the nonnegative difference between the numbers of the regions where the pointer​ stops, and define a probability mass function ​g(x)=​P(X=​x). ​a) State the range of X. ​b) Write g as a set of ordered pairs. ​c) Draw a probability distribution as a histogram. ​d) Find ​g(5​), and explain what this number represents. ​e) Find μ​, and explain what this number represents.

Astandard deck of cards contains 52 cards. one card is selected from the deck. (a) compute the probability of randomly selecting a diamond or heart. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability of randomly selecting a diamond or heart or club. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability of randomly selecting queen or club. (type an integer or a decimal rounded to three decimal places as needed.)