5: Discrete Probability Distributions
- Page ID
- 45477
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- A discrete probability distribution lists all possible outcomes of a random variable along with their probabilities. It helps model real-world scenarios like rolling the dice or counting items. From it, you can calculate the mean (average outcome), variance (spread of values), standard deviation (typical distance from the mean), and expected value.
- 5.2: Binomial Probability Distribution
- The binomial probability distribution models the number of successes in a fixed number of repeated, independent trials with only two outcomes (success or failure). It's used to find the likelihood of a specific number of successes. To compute it, you consider the total trials, the success probability, and how many successes you want.
- 5.3: Mean, Variance, and Standard Deviation of the Binomial Distribution
- To compute the mean, multiply the number of trials by the probability of success. The variance measures how spread out the outcomes are and depends on both success and failure probabilities. The standard deviation is the square root of the variance, showing the typical distance from the mean.
- 5.4: Poisson Distribution
- The Poisson distribution models the number of times an event occurs in a fixed interval of time or space when events happen independently and at a constant rate. It's used for rare events like phone calls per hour or accidents per day. To compute probabilities, you need the average number of occurrences in that interval.
- 5.5: Chapter 5 Formulas
- This section displays the key formulas from Chapter 5, which focus on discrete and binomial probability distributions. Included are the formulas for mean, variance, and standard deviation for both types of distributions. It also covers the formula for expected value and the binomial probability formula, providing the tools needed to analyze and interpret probability-based data.
- 5.6: Chapter 5 - Key Terms and Symbols
- In this section, all the key terms and symbols related to discrete probability distributions are provided for easy access and reference. These include important concepts such as expected value, binomial probability, and types of variables, along with the standard symbols used to represent them. This overview helps organize and clarify the foundational elements of probability theory and statistics.