Explain the Central Limit Theorem (CLT) and why it is useful.

The Central Limit Theorem states that the distribution of the sample mean will approximate a normal distribution as the sample size increases, regardless of the original population distribution. Specifically, if $X$ is any random variable, then as $n \to \infty$, the sample mean $\bar X \sim \mathcal{N}(\mu, \sigma^2 / n)$. In data-rich environments like tech companies, CLT enables experimentation platforms to analyze user behavior.

For example, when testing whether a feature increases DAU, each user outcome $X_i \sim \mathrm{Bernoulli}(p)$. With a large enough sample, we can apply CLT to make inferences about population parameters $\mu$ and $\sigma^2$ using sample statistics, making it essential for A/B testing and hypothesis testing.