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 =

For each variable, the possible values are:

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}

Item a:

In total, there are 10 pumps, hence the possible values are all integers from o to 10, that is:

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

Item b:

In the first there are 6 pumps, in the second 4, hence, the difference ranges from -4 to 6, that is:

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

Item c:

The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.

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

Item d:

Either none of the stations have exactly two pumps in use, or one has, or both, hence the variable ranges from 0 to 2.

Z = {0, 1, 2}

A similar problem is given at link