L05.3 Probability Mass Functions

TL;DR

A probability mass function (PMF) describes the likelihood of different values for a discrete random variable, with examples and calculations provided.

Transcript

A random variable can take different numerical values depending on the outcome of the experiment. Some outcomes are more likely than others, and similarly some of the possible numerical values of a random variable will be more likely than others. We restrict ourselves to discrete random variables, and we will describe these relative likelihoods in ... Read More

Key Insights

• ⚾ A random variable can take different numerical values based on the outcome of an experiment.
• 💆 The probability mass function (PMF) describes the probabilities of these values.
• ❓ The PMF is a function that assigns probabilities to each possible value of the random variable.
• 🪜 The probabilities of all possible values of the random variable should add up to 1.
• 🚱 The PMF is always non-negative since probabilities are non-negative.
• ❓ The PMF can be plotted to visualize the probabilities of different values.
• 🪜 The PMF is calculated by considering each possible value of the random variable and adding the probabilities of the corresponding outcomes.

Questions & Answers

Q: What is a random variable?

A random variable is a variable that takes on different numerical values based on the outcome of an experiment or event. It represents uncertainty in the outcome.

Q: What does the probability mass function (PMF) describe?

The PMF describes the probabilities assigned to each possible value of a random variable in a discrete probability distribution.

Q: How is the PMF calculated?

To calculate the PMF, we consider each possible value of the random variable one at a time and find the outcomes for which the random variable takes on that specific value. We then add the probabilities of those outcomes.

Q: What are the properties of the PMF?

The PMF is non-negative for all values of the random variable. Additionally, the sum of the probabilities for all possible values of the random variable should be equal to 1.

Summary & Key Takeaways

• A random variable can take different numerical values based on the outcome of an experiment, and the PMF describes the probability of these values.

• The PMF is a function that assigns probabilities to each possible value of the random variable.

• The probabilities of all possible values should add up to 1.