About this topic
Before you begin
Work with probability density and cumulative distribution functions, and uniform and exponential models.
Learning goals
- Use probability density and cumulative distribution functions, expectations, medians and modes
- Use uniform and exponential models and relate exponential waiting times to Poisson counts
Syllabus statements covered
- Include: probability density function of a continuous random variable and its mean and variance (includes ‘piecewise’ probability density function); cumulative distribution function and its relationship with the probability density function; concepts of median and mode of a continuous random variable; use of the result E(g(X)) = ∫_−∞^∞ g(x) f(x) dx in simple cases, where f(x) is the probability density function of X and g(x) is a function of X; uniform distribution and exponential distribution as probability models; relationship between Poisson and exponential distributions.
In this topic
Density functions and exponential models
Work with probability density and cumulative distribution functions, medians and modes, and uniform and exponential models.