Question 1025116
 
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.