The probability equation for a survey on the number of speeding tickets given on a certain day in a local neighborhood is given as (where x can be 0, 1, 2, or 3). Does this determine a probability distribution? Why or why not?(1 point)ResponsesYes, because the sum of all the probabilities is 1.Yes, because the sum of all the probabilities is 1.Yes, because the sum of all the probabilities is not 1.Yes, because the sum of all the probabilities is not 1.No, because the sum of all the probabilities is 1.No, because the sum of all the probabilities is 1.No, because the sum of all the probabilities is not 1.

Question

The probability equation for a survey on the number of speeding tickets given on a certain day in a local neighborhood is given as   (where x can be 0, 1, 2, or 3). Does this determine a probability distribution? Why or why not?(1 point)ResponsesYes, because the sum of all the probabilities is 1.Yes, because the sum of all the probabilities is 1.Yes, because the sum of all the probabilities is not 1.Yes, because the sum of all the probabilities is not 1.No, because the sum of all the probabilities is 1.No, because the sum of all the probabilities is 1.No, because the sum of all the probabilities is not 1.

GPT-4o mini · Answer

To determine whether the given information forms a probability distribution, we need to check two main criteria:

Each probability must be non-negative: \( P(x) \geq 0 \) for each possible outcome (in this case, for \( x = 0, 1, 2, 3 \)).
The sum of all probabilities must equal 1: \( P(0) + P(1) + P(2) + P(3) = 1 \).

From your description, it seems there should be a specific probability distribution given or implied. However, without the actual probabilities provided for \( P(0), P(1), P(2), \) and \( P(3) \), I can't directly assess if it is indeed a probability distribution.

To answer your question:

If the sum of the probabilities for \( x = 0, 1, 2, 3 \) equals 1, and all individual probabilities are non-negative, then Yes, this does determine a probability distribution.
If the sum is not equal to 1, or if any individual probability is negative, then No, this does not determine a probability distribution.

Based on this context, you should select an answer that corresponds to these explanations. If you were to choose from your options without specific probabilities presented, you would look for "Yes, because the sum of all the probabilities is 1." or "No, because the sum of all the probabilities is not 1." depending on whether the required conditions are satisfied.