The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.) a. T = the total number of pumps in use b. T = X = the difference between the numbers in use at stations 1 and 2 X = c. U = the maximum number of pumps in use at either station U = d. Z = the number of stations having exactly two pumps in use Z =

a. T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b. X = { - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6}

c. U = {0, 1, 2, 3, 4, 5, 6}

d. Z = {0, 1, 2}

Step-by-step explanation:

n1 = 6 pumps

n2 = 4 pumps

a. The total number of pumps in use:

The number of pumps in use can range from 0 (no pumps used in both stations) to 10 (all pumps used in both stations), assuming all integers in between. Thus, the set T is:

T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b. The difference between the numbers in use at stations 1 and 2 can range from - 4 (no pumps in station 1 and all pumps in station 2 being used) to 6 (all pumps in station 1 and no pumps in station 2 being used), assuming all integers in between. Thus, the set X is:

X = { - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6}

c. The maximum number of pumps in use at either station is given by the possible numbers of pumps at use in station 1 (From 0 to 6). The set U is:

U = {0, 1, 2, 3, 4, 5, 6}

d. The number of stations having exactly two pumps in use can be neither, one or both. The set Z is:

Z = {0, 1, 2}