Continuous random variables, sampling and advanced inference

By the end you’ll be able to

• Define and use a probability density function, including finding unknown constants and calculating probabilities by integration over intervals.
• Calculate the cumulative distribution function, expectation and variance of a continuous random variable where required.
• Use the distribution of the sample mean, including $$\bar X\sim N\left(\mu,\frac{\sigma^2}{n}\right)$$ when sampling from a normal population or under stated conditions.