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Random Variables

Random variables are functions with numerical outcomes that occur with some level of uncertainty. For example, rolling a 6-sided die could be considered a random variable with possible outcomes {1,2,3,4,5,6}.

Introduction to Probability Distributions
Lesson 1 of 2
  1. 1
    A random variable is, in its simplest form, a function. In probability, we often use random variables to represent random events. For example, we could use a random variable to represent the outc…
  2. 2
    ##### Discrete Random Variables Random variables with a countable number of possible values are called discrete random variables. For example, rolling a regular 6-sided die would be considered a…
  3. 3
    A probability mass function (PMF) is a type of probability distribution that defines the probability of observing a particular value of a discrete random variable. For example, a PMF can be use…
  4. 4
    The binom.pmf() method from the scipy.stats library can be used to calculate the PMF of the binomial distribution at any value. This method takes 3 values: - x: the value of interest - n: the numb…
  5. 5
    We have seen that we can calculate the probability of observing a specific value using a probability mass function. What if we want to find the probability of observing a range of values for a disc…
  6. 6
    We can use the same binom.pmf() method from the scipy.stats library to calculate the probability of observing a range of values. As mentioned in a previous exercise, the binom.pmf method takes 3 va…
  7. 7
    The cumulative distribution function for a discrete random variable can be derived from the probability mass function. However, instead of the probability of observing a specific value, the cumul…
  8. 8
    We can use a cumulative distribution function to calculate the probability of a specific range by taking the difference between two values from the cumulative distribution function. For example, to…
  9. 9
    We can use the binom.cdf() method from the scipy.stats library to calculate the cumulative distribution function. This method takes 3 values: - x: the value of interest, looking for the probability…
  10. 10
    Similar to how discrete random variables relate to probability mass functions, continuous random variables relate to probability density functions. They define the probability distributions of cont…
  11. 11
    We can take the difference between two overlapping ranges to calculate the probability that a random selection will be within a range of values for continuous distributions. This is essentially the…
  12. 12
    Congrats! We have finished our introduction to probability distributions! To review, we have: * Learned about different types of random variables * Calculated the probability of specific events us…

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