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.

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

hm let me think hm think think hm think yes