SOLUTION: Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x 1 2 3 4 P(x) 0.01 7/12 1/12

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Question 576097: Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
(A)
x
1
2
3
4

P(x)
0.01
7/12
1/12
1/4


(B)
x
3
6
8

P(x)
0.24
3/5
0.135


(C)
x
20
30
40
50

P(x)
0.33
0.02
-0.04
0.69
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started

A)

If the sums of all the individual probabilities add to 1 and each probability is positive (and less than 1), then this is a valid probability distribution. So let's add up the individual probabilities

P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

0.01 + 7/12 + 1/12 + 1/4

0.926666667

So the probabilities all add to 0.926666667, which is NOT 1.

So this is NOT a valid probability distribution.
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