Posts tagged: undergraduate
The Monty Hall Problem: Why You Should Always Switch
The conditional probability problem that has produced more confident wrong answers than almost any other. The correct answer is 2/3, and the host's knowledge is why.
Variance and Standard Deviation: Why Spread Matters
Two distributions with identical means can behave entirely differently. Variance and standard deviation measure why, and understanding the mechanics behind them reveals what they actually capture.
What a p-value Actually Measures
A p-value is not the probability the null hypothesis is true, not a measure of effect size, and not a verdict on whether a finding is real. Here is what it is.
The Binomial Distribution: Counting Successes in Fixed Trials
How the binomial distribution models the number of successes in a fixed number of independent trials, and why the formula looks the way it does.
The Poisson Distribution: Modeling Rare Events at a Known Rate
The Poisson distribution models counts of independent events occurring at a constant rate. One parameter does everything, and that turns out to be enough.
The Central Limit Theorem: Why Averages Behave
Individual observations can follow nearly any distribution. Average enough of them together, and the result converges toward normal. Here's why that happens and why it matters.
Regression to the Mean: Why Exceptional Performance Doesn't Last
Extreme outcomes tend to be followed by more ordinary ones. This is not a psychological phenomenon. It is a mathematical one, with real implications for how we evaluate causes and interventions.
Type I and Type II Errors: The Trade-Off You Can't Avoid
False positives and false negatives are not both minimizable at once. The threshold that reduces one will increase the other. Where it gets set is a choice, and it matters.
What Confidence Intervals Actually Tell You
A 95% confidence interval does not mean a 95% probability that the true value is inside it. Here is what the statement actually means, and why the distinction is worth getting right.
Discrete vs Continuous Distributions: PMF, PDF, and CDF
The difference between discrete and continuous probability distributions, explained through the PMF, PDF, and CDF, with cat examples that are doing actual work.