https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/random-variables 2020-07-26T09:23:46Z Random variables Basic idea and definitions of random variables Sal Khan video https://cdn.kastatic.org/googleusercontent/qvRdke9M6v3Qpb1vuYZsEoZeINwGrsvcCs5yqZEV5wjs2Tq6BO4aQY1pMvIrKOTHrONu5sjnmgucCBokWEAt1MJ_ Random variables Basic idea and definitions of random variables https://cdn.kastatic.org/ka-youtube-converted/3v9w79NhsfI.mp4/3v9w79NhsfI.mp4 332 Variables aleatorias discretas https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/discrete-and-continuous-random-variables 2022-11-16T04:22:43.7414897Z Discrete and continuous random variables Discrete random variables can only take on a finite number of values. For example, the outcome of rolling a die is a discrete random variable, as it can only land on one of six possible numbers. Continuous random variables, on the other hand, can take on any value in a given interval. For example, the mass of an animal would be a continuous random variable, as it could theoretically be any non-negative number. Sal Khan video https://cdn.kastatic.org/googleusercontent/C-EUxA7o10ncTqWb2z3f09iyZER2yjTS385EnCOZNmur3MrWqHqiONcNUW0u6_lNg8yGeV8CPihpCspEs_uo-J5z Discrete and continuous random variables Discrete random variables can only take on a finite number of values. For example, the outcome of rolling a die is a discrete random variable, as it can only land on one of six possible numbers. Continuous random variables, on the other hand, can take on any value in a given interval. For example, the mass of an animal would be a continuous random variable, as it could theoretically be any non-negative number. https://cdn.kastatic.org/ka-youtube-converted/dOr0NKyD31Q.mp4/dOr0NKyD31Q.mp4 717 Variables aleatorias discretas https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:probability-distributions-introduction/v/discrete-probability-distribution 2021-07-01T17:39:49Z Constructing a probability distribution for random variable Sal breaks down how to create the probability distribution of the number of "heads" after 3 flips of a fair coin. Sal Khan video https://cdn.kastatic.org/googleusercontent/aTcNbv9GQotylfLCmyyZtX9Djm9ubldaRcwp7oJOLS1R9HeCPdWS8leJi3KDvju6_5stm7Ki_0aUHPzvx7vOIc0 Constructing a probability distribution for random variable Sal breaks down how to create the probability distribution of the number of "heads" after 3 flips of a fair coin. https://cdn.kastatic.org/ka-youtube-converted/cqK3uRoPtk0.mp4/cqK3uRoPtk0.mp4 408 Variables aleatorias discretas https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/e/constructing-probability-distributions 2026-04-08T00:36:09.500768563Z Constructing probability distributions Given a context, create a probability distribution. Ben Stenhaug exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-theoretical-and-experimental-probability/v/constructing-probability-model-from-observations 2021-04-13T21:46:08Z Probability models example: frozen yogurt Model the probability of a frozen yogurt line having 0, 1, or 2 people in it. video https://cdn.kastatic.org/googleusercontent/HXlJ4PHRMOBTZ-bge_Vb7nfjT-AFAW3HD_JKKoXfO7WMwCi_v-Y2H92BNptoNt997l7xOsaCIkdnh966zEO8_BO6 Probability models example: frozen yogurt Model the probability of a frozen yogurt line having 0, 1, or 2 people in it. https://cdn.kastatic.org/ka-youtube-converted/BIpsQIJUCC8.mp4/BIpsQIJUCC8.mp4 445 Variables aleatorias discretas https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-theoretical-and-experimental-probability/e/probability-models 2026-03-26T05:20:35.16058035Z Probability models Practice creating probability models and understand what makes a valid probability model. Rhonda Hughes exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:probability-distributions-introduction/v/valid-discrete-probability-distribution-examples 2022-10-07T00:22:18.752150461Z Valid discrete probability distribution examples Worked examples on identifying valid discrete probability distributions. video https://cdn.kastatic.org/ka_thumbnails_cache/c502cd0f-37e8-449d-8549-17e09a110b87_1280_720_base.png Valid discrete probability distribution examples Worked examples on identifying valid discrete probability distributions. https://cdn.kastatic.org/ka-youtube-converted/uXtxKxYl1Iw.mp4/uXtxKxYl1Iw.mp4 240 Variables aleatorias discretas https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:probability-distributions-introduction/v/example-analyzing-discrete-probability-distribution 2022-10-07T00:22:18.752150461Z Probability with discrete random variable example Example analyzing discrete probability distribution video https://cdn.kastatic.org/ka_thumbnails_cache/afed432b-948b-4167-9ccd-583258ae515b_1280_720_base.png Probability with discrete random variable example Example analyzing discrete probability distribution https://cdn.kastatic.org/ka-youtube-converted/d2STHFVHGAg.mp4/d2STHFVHGAg.mp4 230 Variables aleatorias discretas https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:probability-distributions-introduction/e/probability-discrete-random-variables 2026-03-25T22:20:39.096098541Z Probability with discrete random variables Practice calculating probabilities in the distribution of a discrete random variable. Jeff Dodds exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:expected-value/v/expected-value-of-a-discrete-random-variable 2022-10-07T00:22:18.752150461Z Mean (expected value) of a discrete random variable We can calculate the mean (or expected value) of a discrete random variable as the weighted average of all the outcomes of that random variable based on their probabilities. We interpret expected value as the predicted average outcome if we looked at that random variable over an infinite number of trials. video https://cdn.kastatic.org/ka_thumbnails_cache/74a42b52-15cb-443c-bd3d-cd165775c4c0_1280_720_base.png Mean (expected value) of a discrete random variable We can calculate the mean (or expected value) of a discrete random variable as the weighted average of all the outcomes of that random variable based on their probabilities. We interpret expected value as the predicted average outcome if we looked at that random variable over an infinite number of trials. https://cdn.kastatic.org/ka-youtube-converted/qafPcWNUiM8.mp4/qafPcWNUiM8.mp4 272 Variables aleatorias discretas https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/a/expected-value-basic 2021-04-29T07:58:49Z Expected value (basic) article https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/e/expected_value 2026-03-24T23:41:07.080866137Z Expected value Compute the expected value given a set of outcomes, probabilities, and payoffs Mark Wittels exercise https://www.khanacademy.org/math/ap-statistics/random-variables-ap/xfb5d8e68:mean-standard-deviation-random-variables/v/variance-and-standard-deviation-of-a-discrete-random-variable 2024-01-19T18:34:27.70568811Z Variance and standard deviation of a discrete random variable We learn how to calculate the mean and standard deviation of a discrete random variable. The concept of a random variable is explained, along with methods to calculate its expected value (mean) and measure its spread (variance and standard deviation). A practical example makes the concept easier to understand. video https://cdn.kastatic.org/ka_thumbnails_cache/1480a2e2-c783-4cc6-b18d-f26efd6e3e77_1280_720_base.png Variance and standard deviation of a discrete random variable We learn how to calculate the mean and standard deviation of a discrete random variable. The concept of a random variable is explained, along with methods to calculate its expected value (mean) and measure its spread (variance and standard deviation). A practical example makes the concept easier to understand. https://cdn.kastatic.org/ka-youtube-converted/2egl_5c8i-g.mp4/2egl_5c8i-g.mp4 386 Variables aleatorias discretas https://www.khanacademy.org/math/ap-statistics/random-variables-ap/xfb5d8e68:mean-standard-deviation-random-variables/e/standard-deviation-discrete-random-variable 2021-07-01T02:19:28Z Standard deviation of a discrete random variable Practice calculating the standard deviation of a discrete random variable. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/random-variables-ap/xfb5d8e68:mean-standard-deviation-random-variables/a/interpret-mean-standard-deviation-discrete-random-variable 2021-07-01T02:19:30Z Mean and standard deviation of a discrete random variable Practice calculating and interpreting the mean and standard deviation of a discrete random variable. article