Discrete Random Variables and Their Probability Distributions
Statistics • 11 topics in this chapter.
Discrete Random Variables and Their Probability Distributions on STEM Calculators is a statistics chapter that helps you model outcomes that take countable values, such as the number of successes, defects, or events. It includes tools for building and checking discrete probability distributions (pmf tables), computing cumulative probabilities, and finding key summaries like the expected value (mean), variance, and standard deviation, along with support for widely used discrete models such as the binomial and related counting-based distributions.
This chapter is ideal for beginners transitioning from basic probability into random variables, and it also supports intermediate and advanced learners who want faster, more reliable calculations for coursework and exams. Teachers can generate correct distribution tables and example problems, self-learners can follow step-by-step explanations to understand how probabilities and summaries are constructed, and advanced users can quickly validate models for quality control, reliability, and simple risk analysis.
Enter a probability mass function, counts, or distribution parameters to instantly compute probabilities, cumulative values, and descriptive measures of the random variable. With clear outputs that explain what each result means, this page helps you connect real-world scenarios to discrete probability distributions and build confidence before moving on to continuous distributions and statistical inference.
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1. Probability Distribution of a Discrete Random Variable
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2. Mean of Discrete Random Variable
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3. Standard Deviation of a Discrete Random Variable
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4. Factorials Combinations and Permutations
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5. The Binomial Probability Distribution
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6. Using the Table of Binomial Probabilities
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7. Probability of Success and the Shape of Binomial Distribution
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8. Mean and Standard Deviation of Binomial Distribution
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9. The Hypergeometric Probability Distribution
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10. The Poisson Probability Distribution
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11. Using the Table of Poisson Probabilities
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