- Belleview High School
- AICE Mathematics II with Statistics II
- Unit 11 - Linear Combinations of Random Variables
LOSITO, MICHAEL
Page Navigation
- Teacher Homepage
- Meet the Teacher
-
AICE Mathematics I with Statistics I
- Unit 1 - Quadratics
- Unit 2 - Functions and Graphs
- Unit 3 - Coordinate Geometry
- Unit 4 - Trigonometry
- Unit 5 - Sequences and Series
- Unit 6 - Differentiation
- Unit 7 - Integration
- Unit 8 - Representation, Location and Spread
- Unit 9 - Probability
- Unit 10 - Distributions
- Unit 11 - The Normal Distribution
-
AICE Mathematics II with Statistics II
- Unit 1 - Algebra
- Unit 2 - Exponential and Logarithmic Functions
- Unit 3 - Trigonometry
- Unit 4 - Numerical Solutions
- Unit 5 - Differentiation
- Unit 6 - Vectors
- Unit 6 - Vectors
- Unit 7 - Binomial Expansion and Rational Functions
- Unit 8 - Complex Numbers
- Unit 9 - Integration & Differential Equations
- Unit 10 - The Poisson Distribution
- Unit 11 - Linear Combinations of Random Variables
- Unit 12 - Continuous Random Variables
- Unit 13 - Sampling and Estimation
- Unit 14 - Hypothesis Testing
- Pre AICE Mathematics 3 (IGCSE)
- Pre AICE Physics
- AICE MATH I - Practice Papers
- AICE MATH II - Practice Papers
- AICE Math Resources
-
Chapter 2 – Linear Combinations of Random Variables
When students have completed this lesson they should be able to:
- E(aX + b) = aE(X) + b and Var(aX + b) = a^2Var(X)
- E(aX + bY) = aE(X) + bE(Y)
- Var(aX + bY) = a^2Var(X) + b^2Var(Y) for independent X and Y
- If X has a normal distribution, then so does aX + b
- Is X and Y have independent normal distributions, then aX + bY has a normal distribution
- If X and Y have independent Poisson distributions, the X + Y has a Poisson distribution