Question

To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.
a. List the experimental outcomes associated with performing the blood analysis.


- Select your answer -
b. Let denote the total number of steps required to do the complete analysis (both procedures). Show what value of random variable will assume for each of the experimental outcomes. (If an outcome does not occur, enter “0”.)

Experimental Outcomes Value of
(1)
(2)
(3)
(1, 1)
(1, 2)
(1, 3)
(2, 1)
(2, 2)
(2, 3)
(3, 1)
(3, 2)
(3, 3)

Answer 1

The random numbers can take any value randomly.

A simple random sample is selected in such a manner that each unit has the equal probability of being included in the sample.

The possible outcomes of the given experiment are

(1, 1)  ,(1, 2) , (1, 3) , (2, 1) , (2, 2) , (2, 3)                                      

The first procedure requires either one or two separate steps.

This means it cannot take the third step in the first procedure.

Let 1 take the first  and the second  step.

So if 1 occurs then 1,2,  can occur and 3 cannot occur.

Similarly

If 2 occurs then 1,2, and 3 can occur.

The second procedure requires either one, two, or three steps.

Therefore

Experimental Outcomes         Value of  x

(1)                                                         0   Not possible  2 process required

(2)                                                     0          Not possible

(3)                                                        0        Not possible

(1, 1)                                           2

(1, 2)                                          3

(1, 3)                                         4

(2, 1)                                        3

(2, 2)                                        4

(2, 3)                                       5

(3, 1)                                      0                  Not possible  process 1 cannot take 3

(3, 2)                                     0               Not possible

(3, 3)                                     0               Not possible

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