Maths Continuous Distributions

Maths Continuous Distributions

1. Probability Density Functions

   • Area
     • The area under a probability density function curve is equal to 1.
   • Median
     • The area between the median value and the lowest value is equal to 0.5.
   • Mean
     • The mean is equal to the integral of xf(x).
   • Variance
     • The variance is equal to the integral of x^2 f(x), then subtracted by [E(x)]^2.
   • Mode
     • The mode is equal to the highest value on the graph, where the gradient is equal to 0.

2. Cumulative Distribution Functions

   • Integrate Probability Density Function
   • Be aware of the range of the CDF, as you must state that the function below the lowest value is equal to 0 and the function above the highest value is equal to 1.