Question

three students scheduled interviews for summer employment at the brookwood institute. in each case, the interview results in either an offer for a position or no offer. experimental outcomes are defined in terms of the results of the three interviews: y = \yes, the student receives an offer\ and n =
o, the student does not receive an offer.\ a. list the experimental outcomes. b. let x equal the number of offers made. is x continuous or discrete? c. show the value of the random variable x for each of the experimental outcomes. if your answer is zero or the experimental outcome does not occur, enter \0\.

Explanation:

Step1: Recall the definition of random - variable value

The random variable $x$ is the number of offers made. Count the number of 'Y's in each experimental outcome to find the value of $x$.

Step2: Calculate for each outcome

• For $(N,N,Y)$: There is 1 'Y', so $x = 1$.
• For $(N,N,N)$: There are 0 'Y's, so $x = 0$.
• For $(N,Y,N)$: There is 1 'Y', so $x = 1$.
• For $(Y,Y,N)$: There are 2 'Y's, so $x = 2$.
• For $(N,Y,Y)$: There are 2 'Y's, so $x = 2$.
• For $(Y,Y,Y)$: There are 3 'Y's, so $x = 3$.
• For $(Y,N,Y)$: There are 2 'Y's, so $x = 2$.
• For $(Y,N,N)$: There is 1 'Y', so $x = 1$.

Answer:

Experimental Outcome	Value of $x$
$(N,N,N)$	0
$(N,Y,N)$	1
$(Y,Y,N)$	2
$(N,Y,Y)$	2
$(Y,Y,Y)$	3
$(Y,N,Y)$	2
$(Y,N,N)$	1