Question 1025116: I wish there was an easier way to show you the question but the only way I can think of is to just type them out. I tried lining up the numbers together to make it look like a table but the website keeps pushing them in. I hope you can understand it.
Question: Which of the following could not be a probability distribution?
1.) Outcomes: 1, 2, 3, 4
Probability: 0.10, 0.15, 0.25, 0.5
2.)Outcomes: 1, 2, 3, 4
Probability: 0.97, 0.01, 0.01, 0.01
3.)Outcomes: 1, 2, 3, 4
Probability:0.32, 0.42, 0.25, 0.1
4.)Outcomes: 1, 2, 3, 4
Probability:0.43, 0.21, 0.2, 0.16
Found 2 solutions by FrankM, mathmate:
Answer by FrankM(1040)   (Show Source):
You can put this solution on YOUR website! It looks fine.
You see how 3) 0.32, 0.42, 0.25, 0.1 adds to 1.09?
That can't be. The percents or probabilities must add to 100%, or 1.00
Answer by mathmate(429)  (Show Source):
You can put this solution on YOUR website!
Question:
I wish there was an easier way to show you the question but the only way I can think of is to just type them out. I tried lining up the numbers together to make it look like a table but the website keeps pushing them in. I hope you can understand it.
Question: Which of the following could not be a probability distribution?
1.) Outcomes: 1, 2, 3, 4
Probability: 0.10, 0.15, 0.25, 0.5
2.)Outcomes: 1, 2, 3, 4
Probability: 0.97, 0.01, 0.01, 0.01
3.)Outcomes: 1, 2, 3, 4
Probability:0.32, 0.42, 0.25, 0.1
4.)Outcomes: 1, 2, 3, 4
Probability:0.43, 0.21, 0.2, 0.16
Solution:
No problem. The question is quite understandable.
The key point here is that ANY probability distribution has the property that the sum of the probabilities of ALL the outcomes (for a discrete distribution), or the integral representing the area under the distribution should equal exactly one, not more, not less.
Examples:
x 1,2,3,4
P(x) 0.1,0.2,0.3,0.4
can be a probability distribution, because the sum of the probabilities of all possible outcomes (0.1+0.2+0.3+0.4)=1.
while
x -1,0,+1
P(x) 0.2, 0.3, 0.2
cannot be a probability distribution because 0.2+0.3+0.2=0.7 ≠ 1.
Proceeding along these lines, you will have no trouble spotting the "intruder" among the choices.
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