The number of pumps in use at both a six-pump station and a four-pump station wi
ID: 3276268 • Letter: T
Question
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: a) T= the total number of pumps in use (ALREADY FIGURED OUT) b) X= the difference between the numbers in use at stations 1 and 2. (Answer is 11, how???)
c) U= maximum number of pumps in use at either station (Answer is 7 values, how?)
d) Z= the number of stations having exactly two pumps in use ( Answer is 3 values in range, how??)
Explanation / Answer
Total number of pumps in both station is 4+6=10
a)
Now T shows the total number of pumps that is working. Here T can take values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
That is T can take 11 different values as follows:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
(b)
Let X1 shows the number of pumps working on station1. So X1 can take values 0, 1, 2, 3, 4, 5, 6
Let X2 shows the number of pumps working on station2. So X2 can take values 0, 1, 2, 3, 4
So the difference between the numbers in use at stations 1 and 2 is
X = X1- X2
For example when X1 = 0 and X2 =4 then X = -4
when X1 = 0 and X2 =3 then X = -3
Likewise possible values X can take is as follows:
X = -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6
(C)
Let X1 shows the number of pumps working on station1. So X1 can take values 0, 1, 2, 3, 4, 5, 6
Let X2 shows the number of pumps working on station2. So X2 can take values 0, 1, 2, 3, 4
Here U shows the maximum value of X1 and X2. Here U can take following values:
U = 0, 1, 2, 3, 4, 5, 6
d)
Either at both station two pumps used, or at one station two pumps used and or at zero station exactly 2 pumps used.
So possible values of Z are 0, 1, 2
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Following table shows the possible values of X1 and X2 and possible values of X and U:
X1 X2 U=max(X1, X2) X=X1-X2 0 0 0 0 1 0 1 1 2 0 2 2 3 0 3 3 4 0 4 4 5 0 5 5 6 0 6 6 0 1 1 -1 1 1 1 0 2 1 2 1 3 1 3 2 4 1 4 3 5 1 5 4 6 1 6 5 0 2 2 -2 1 2 2 -1 2 2 2 0 3 2 3 1 4 2 4 2 5 2 5 3 6 2 6 4 0 3 3 -3 1 3 3 -2 2 3 3 -1 3 3 3 0 4 3 4 1 5 3 5 2 6 3 6 3 0 4 4 -4 1 4 4 -3 2 4 4 -2 3 4 4 -1 4 4 4 0 5 4 5 1 6 4 6 2