Question

part 1: probability review
there is a limit to the number of pumpkins customers can purchase at patricks pumpkin paradise. each customer can purchase a maximum of 10 pumpkins. naturally, not all customers purchase exactly 10 pumpkins, but all customers purchase at least one pumpkin. patrick keeps very detailed records about the number of pumpkins each of his customers purchases, and he put the following probability model together based on these records. please use this information to answer questions 1 through 6.

1. what are two things about the above probability model that make this a legitimate model? please explain.

Explanation:

A legitimate probability model must satisfy two conditions:

1. Each probability \(P(x)\) is between \(0\) and \(1\) (inclusive). Looking at the given probabilities \(0.14,0.21,0.19,0.17,0.13,0.04,0.06,0.02,0.03,0.01\), all of them are in the interval \([0,1]\).
2. The sum of all probabilities is equal to \(1\). Let's calculate the sum:

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Answer:

1. All probabilities \(P(x)\) satisfy \(0\leq P(x)\leq1\).
2. The sum of all probabilities \(\sum_{x = 1}^{10}P(x)=1\).