Random variable
A random variable is a function that assigns numerical values to outcomes of a random process and is characterized by a probability distribution.
Math and Architectures of Deep Learning
A quantity whose possible values are associated with probabilities, used to model uncertain measurable attributes or event outcomes.
- How it is used
- Models uncertain quantities and event outcomes as inputs to probability distributions and machine-learning probability calculations.
- How deep it goes
- Develops discrete and continuous definitions, densities, sampling, expectations, joint variables, and distribution examples with formulas and PyTorch code.
- Examples
- Uses quantized adult weights and heights, uniform intervals, Bernoulli trials, binomial success counts, and four-class image predictions.
- What you can do after
- Apply it via PyTorch distributions to evaluate probabilities, draw samples, and compare empirical moments with distribution properties.
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Statistics Every Programmer Needs
A random variable is a function that assigns numerical values to outcomes of a random experiment.
- How it is used
- Uses numerical outcomes to model uncertainty for probability calculations and staffing simulations.
- How deep it goes
- Defines discrete and continuous values, explains their probability functions, and works through dice-sum PMF and CDF calculations.
- Examples
- Works through two-dice sums and uses call-center absentee counts to motivate simulation.
- What you can do after
- Practice/perform discrete probability calculations and evaluate/understand simulated outcomes for decisions under uncertainty.
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Causal AI
A random variable is a variable whose possible values and uncertainty are described by a probability distribution.
- How it is used
- Represents uncertain outcomes so probability distributions, recorded data, and causal interventions can be expressed in a common notation.
- How deep it goes
- Defines discrete outcomes and probability values, then extends to expectations and dependence; mentions continuous densities without working through integration.
- Examples
- Uses die rolls and coin flips for outcomes, plus a three-state probability table implemented with pgmpy.
- What you can do after
- Apply it via pgmpy DiscreteFactor to represent a finite-outcome distribution and calculate a probability-weighted expectation.
Causal Inference for Data Science
A random variable is a variable whose value is determined by the outcome of a random experiment.
- How it is used
- Distinguishes fixed individual outcomes, sampled population variables, and conditional uncertainty when defining causal quantities.
- How deep it goes
- Defines expectations, variance, empirical distributions, and conditional randomness, but defers deeper statistical inference and confidence-interval methods.
- Examples
- Uses coin tosses, treatment and recovery indicators, potential outcomes, and functional causal-graph relationships.
- What you can do after
- Evaluate/understand probabilities, expectations, and conditional uncertainty without confusing samples, populations, or fixed potential outcomes.
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Bayesian Optimization in Action
A random variable is a variable whose value is determined by an uncertain outcome or probabilistic process.
- How it is used
- Uses random variables to represent multiple uncertain quantities jointly in multivariate Gaussian models.
- How deep it goes
- Defines variables within a Gaussian vector and traces their means, variances, and covariances through matrix entries.
- Examples
- Illustrates random variables with height, IQ, income, birth weight, and a housing-price multivariate example.
- What you can do after
- Evaluate how Gaussian models assign expected values, variances, and covariances to individual uncertain quantities.
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Related concepts
- probability distributionused by · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
- interventionconfigured by · An intervention is a deliberate, externally imposed change or control applied to a variable or system to alter or assess its behavior or outcomes.
- distanceincludes · Distance is a measure of separation between points or entities in a defined space or context.
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