An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The sum of the probabilities equals 1, and each probability is between 0 and 1. Therefore, the distribution is a discrete probability distribution. This is a discrete probability distribution because the sum of the probabilities is 1.0 and each probability is between 0 and 1, inclusive
Explanation
Analyze the problem and data We are given a probability distribution for the random variable X, which represents the number of marriages an individual aged 15 years or older has been involved in. To verify that this is a discrete probability distribution, we need to check two conditions:
The sum of all probabilities must equal 1.
Each individual probability must be between 0 and 1, inclusive.
Calculate the sum of probabilities First, let's calculate the sum of the probabilities:
S = P ( 0 ) + P ( 1 ) + P ( 2 ) + P ( 3 ) + P ( 4 ) + P ( 5 ) = 0.291 + 0.521 + 0.148 + 0.033 + 0.005 + 0.002
The result of this summation is:
S = 1.0
Verify individual probabilities Next, we need to ensure that each probability is between 0 and 1. Looking at the given probabilities:
0 ≤ 0.291 ≤ 1 0 ≤ 0.521 ≤ 1 0 ≤ 0.148 ≤ 1 0 ≤ 0.033 ≤ 1 0 ≤ 0.005 ≤ 1 0 ≤ 0.002 ≤ 1
All probabilities satisfy this condition.
Conclusion Since the sum of the probabilities is 1 and each probability is between 0 and 1, the given distribution is a discrete probability distribution.
Examples
Discrete probability distributions are used in various real-world scenarios, such as modeling the number of cars passing a certain point on a road in an hour, the number of defective items in a batch of products, or the number of customers arriving at a store in a day. In this case, it models the number of marriages an individual has been involved in. Understanding these distributions helps in making informed decisions and predictions.
