Mathematics: Applications and Interpretation · Topic 4: Statistics and probability

AHL4.14 — Transformations of random variables and unbiased estimators

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL4.14.1

   Linear transformation of a random variable

   $E(aX+b)=aE(X)+b$ and $\mathrm{Var}(aX+b)=a^2\mathrm{Var}(X)$.

2. AIAHL4.14.2

   Combinations of several random variables

   Expectation of any linear combination; variance for independent variables.

3. AIAHL4.14.3

   Unbiased estimators of $\mu$ and $\sigma^2$

   $\bar{x}$ estimates $\mu$ and $s_{n-1}^2$ estimates $\sigma^2$.