Use the following distribution to answer the questions below:

The given distribution
[ Select ]
could not
could
be a probability distribution because
[ Select ]
probabilities do NOT sum to one and are all are NOT greater than or equal to zero
probabilities do NOT sum to one and are all greater than or equal to zero
probabilities sum to one and are NOT greater than or equal to zero
probabilities sum to one and are all greater than or equal to zero

Question

Use the following distribution to answer the questions below:

The given distribution 
[ Select ]
could not
could
 be a probability distribution because 
[ Select ]
probabilities do NOT sum to one and are all are NOT greater than or equal to zero
probabilities do NOT sum to one and are all greater than or equal to zero
probabilities sum to one and are NOT greater than or equal to zero
probabilities sum to one and are all greater than or equal to zero

BlackTom AI · Accepted Answer

Let's break down the situation step by step and evaluate what makes a valid probability distribution.

Option A claims: "The given distribution could not be a probability distribution because probabilities do NOT sum to one and are all are NOT greater than or equal to zero." This is not accurate for two reasons. First, the numbers do indeed sum to one: 0.64 + (-0.08) + 0.30 + 0.12 + 0.02 = 1.00. Second, the statement also says they are all NOT greater than or equal to zero, which is true for the value -0.08, but the overall claim about the sum is false. Since part of the reasoning is wrong (they do sum to one), this option is incorrect.

Option B claims: "The given distribution could not be a probability distribution because probabilities sum to one and are NOT greater than or equal to zero." This aligns with the actual issue: the entries include a negative probability (-0.08), which violates the nonnegativity requirement of a probability distribution, even though the numbers do sum to one. Therefore, this option correctly identifies why the distribution cannot be a valid probability distribution.

To assess why the other potential statements would be incorrect if they were chosen:
- If we asserted that probabilities do NOT sum to one, that would be false here since the sum is exactly one. So any claim about the sum not equaling one would be incorrect.
- If we asserted that all probabilities are greater than or equal to zero, that would also be false because of the negative value (-0.08) in the list; a valid distribution cannot have negative probabilities.

In summary, the only statement that accurately describes the issue is that the distribution cannot be a probability distribution due to the presence of a negative probability, even though the sum is one. The negative value violates the nonnegativity condition fundamental to probability measures.

MATH_1026_17235_202501 S25- Final Exam- Requires Respondus LockDown Browser

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Similar Questions

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