A spinner marked off in five equal-sized regions, numbered 1 comma 2 comma 3 comma 4 comma and 5, 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)equalsP(Xequalsx). 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(0), and explain what this number represents. e) Find mu, and explain what this number represents.

mark branliest

step-by-step explanation:

.6 is 1/2 of 12

the answer is actually d. i just took the test

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

the correct answer is c