When you are asked if a probability distribution (table) is valid you need to answer 3 questions.
1. Does the sum of P(x) add up to any number 1 ? other than2. Are there any negative probabilities? 3. Are there any probabilities larger than 1?
0.129+0.257+0.659+0.008+(-0.053) = 1.000 Since we said there are negative probabilities, example 1 is NOT a probability distribution.Example 2:
1. No, the sum of P(x) adds up to 1 0.2+0.2+0.2+0.2+0.2 = 1.000 2. No, there aren't any negative probabilities. The negative numbers are values for x, not the probability of x. 3. No, there aren't any probabilities larger than 1. Since we said No to all of the questions, example 2 is a probability distribution.Example 3:
1. Yes, the sum of P(x) adds up to 0.999 0.2+0.2+0.2+0.2+0.199 = 0.999 2. No, there aren't any negative probabilities. The negative numbers are values for x, not the probability of x. 3. No, there aren't any probabilities larger than 1. Since we said Yes to the first question, example 3 is NOT a probability distribution. |

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