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Classify each random variable as either discrete or continuous. The number of patrons arriving at a restaurant between \ (5:00\; p.m\). and \ (6:00\; p.m\). The number of new cases of influenza in a particular county in a coming month. The air pressure of a tire on an automobile.
- 5.2: Discrete Probability Distributions
Solution. Each probability is a number between 0 and 1; 0 ≤...
- 5.2: Discrete Probability Distributions
Discrete probability distribution is used to give all the possible values of a discrete random variable along with the probabilities. Understand discrete probability distribution using solved examples.
12 Μαρ 2023 · Solution. Each probability is a number between 0 and 1; 0 ≤ 0.2 ≤ 1, 0 ≤ 0.55 ≤ 1, and 0 ≤ 0.25 ≤ 1. The sum of the probabilities adds up to 1; ∑ P (x i) = 0.2 + 0.55 + 0.25 = 1. Yes, this is a valid discrete probability distribution. A random experiment consists of flipping a fair coin three times. Let X = the number of heads that show up.
26 Μαρ 2023 · The probability distribution of a discrete random variable \(X\) is a listing of each possible value \(x\) taken by \(X\) along with the probability \(P(x)\) that \(X\) takes that value in one trial of the experiment.
Example 4.1. A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let X = the number of times per week a newborn baby's crying wakes its mother after midnight. For this example, x = 0, 1, 2, 3, 4, 5.
The set of all possible outcomes of an experiment is called the sample space (or the universal set) and is denoted by ε, and each possible outcome is called a sample point. Therefore, spinning the spinner gives ε = {1, 2, 3, 4, 5, 6, 7, 8}. subset of the sample space is known as an event.
25 Σεπ 2020 · Together, we will work through numerous examples of how to determine if a distribution is a probability distribution, identify probability given the probability mass function, create a discrete probability distribution for a sample set, and find the cumulative distribution function.
