Continuous random variables - AS level Further Maths Statistics

TThese PowerPoints form full lessons of work that together cover the new AS level Further Maths course for the AQA exam board. Together all the PowerPoints include;
A complete set of notes for students
Model examples
Probing questions to test understanding
Class questions including answers
Individual whiteboard work
Links to exercises in ‘AQA approved textbooks by Camb uni Press’ these can easily be edited for your textbook
The PowerPoints can be used in the lesson and also given to students that have missed a lesson
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Statistics – Continuous random variables covers;

• Understand and use a probability density function, f(x), for a continuous distribution and understand the differences between discrete and continuous distributions
• Find the probability of an observation lying in a specified interval
• Find median and quartiles for given probability density function, f(x)
• Find mean, variance and standard deviation for given CRV function, f(x).
• Know the formulae:
  * E(X)=∫x f(x) dx
  * E(X^2 )=∫x^2 f(x) dx
  * Var(X)=E(X^2 )-E(X)^2
• Understand expectation of linear functions of CRVs and know the formulae:
  * E(aX+b)=aE(X)+b
  * Var(aX+b)=a^2 Var(X)
• Know the formula E(g(X))=∫g(x) f(x) dx
• Find the mean, variance and standard deviation of functions of a continuous random variable such as E(5X^3 ), E(18X^(-3) ), Var(6X^(-1) )
• Know that if X and Y are independent (discrete or continuous) random variables then E(X+Y)=E(X)+E(Y) and Var(X+Y)=Var(X)+Var(Y)