E(X) & Var(X) (Continuous) (Cambridge (CIE) A Level Maths): Revision Note

E(X) & Var(X) (Continuous)

What are E(X) and Var(X)?

• E(X)is the expected value, or mean, of a random variable X

  • E(X) is the same as the population mean so can also be denoted by µ

• Var (X) is the variance of the continuous random variable X

  • Standard deviation is the square root of the variance

How do I find the mean and variance of a continuous random variable?

• The mean, for a continuous random variable X is given by

• This is equivalent to  for discrete random variables

• If the graph of has axis of symmetry, x = a , then  E(X) = a

• The variance is given by

• This is equivalent to   for discrete random variables

• Be careful about confusing   and 

  •                 “mean of the squares”

  •        “square of the mean”

  • If you are happy with the difference between these and how to calculate them the variance formula becomes very straightforward

How do I calculate E(g(X))?

• 

• In particular:

  • as seen above