A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. ... a. What is P(X = 1 and Y = 1)? b. Compute P(X ≤ 1 and Y ≤ 1). c. Give a word description of the event {X ≠0 and Y ≠0}, and compute the probability of this event. d. Compute the marginal pmf of X and of Y. Using pX(x), what is P(X ≤ 1)? e. Are X and Y independent rv's? Explain.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

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