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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.

A) How many experimental outcomes exist?
Note: The possible outcomes are Y/N for first interview, and Y/N for 2nd, and Y/N for 3rd interview.
B) Let x equal the number of students who receive an offer. Is x continuous or discrete?
a) It is discrete b) It is continuous c)It is neither discrete nor continuous
C) Show the value of the random variable for the subset of experimental outcomes listed below. Let Y = "Yes, the student receives an offer", and N = "No, the student does not receive an offer."
Experimental Outcome - Value of X
(Y,Y,Y) - ?
(Y,N,Y) - ?
(N,Y,Y) - ?
(N,N,Y) - ?
(N,N,N) - ?
What are the above experimental outcomes?

Respuesta :

MrRoyal

Answer:

a. 8 outcomes

b. Discrete Variable

c. See explanation below

Step-by-step explanation:

a.

Let N = No Offers made

Let Y = Offers made

The Expected outcome are as follows:

NNN, NNY, NYN, YNN, NYY, YNY, YYN, YYY

= 8

b.

Let x = number of offers made

X is said to be discrete if x can take values that are restricted to a defined or limited values

X is said to be continuous if x can take a range of values that is not restricted to any range(i.e. continuous)

Looking at the brief description above, we can conclude that x is discrete

c.

NNN, 0

NNY, 1

NYN, 1

YNN, 1

NYY, 2

YNY, 2

YYN, 2

YYY, 3

Where 0 to 3 represents number of offers at every instance

Part(a):

Then the outcomes can be,

[tex]\{(1,1,1)(1,1,0)(1,0,1)(0,1,1)(1,0,0)(0,1,0)(0,0,1)(0,0,0) \}[/tex]

Part(b):

The correct option is (a).

Part(c):

The outcomes are,

[tex](1,1,1):x=3\\(1,1,0):x=2\\(1,0,1):x=2\\(0,1,1):x=2\\(1,0,0):x=1\\(0,1,0):x=1[/tex]

Experimental outcomes:

Experimental probability, also known as Empirical probability, is based on actual experiments and adequate recordings of the happening of events.

Part(a):

Let the ordered pair (a,b,c) denote the outcome with a,b,c taking either 1 if the position is offered

Or 0  if the position is not offered.

Then the outcomes can be,

[tex]\{(1,1,1)(1,1,0)(1,0,1)(0,1,1)(1,0,0)(0,1,0)(0,0,1)(0,0,0) \}[/tex]

Part(b):

Let, [tex]x[/tex] is number probability function offers made.

The variable is discrete taking 0 or 1 or 2 or 3 as values.

So, the correct option is (a)

Part(c):

The outcomes are,

[tex](1,1,1):x=3\\(1,1,0):x=2\\(1,0,1):x=2\\(0,1,1):x=2\\(1,0,0):x=1\\(0,1,0):x=1[/tex]

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