Linear Transformations of DRVs (Edexcel A Level Further Maths) : Revision Note
E(X) & Var(X) of aX+b
What are the formulae for E(aX ± b) and Var(aX ± b)?
If
and
are constants then
is a linear transformation of
These are two important formulae:
If values of
are multiplied by
, then
the mean is multiplied by
the variance is multiplied by
as variance is the square of the spread (standard deviation)
If an amount
is added to
is added to the mean
the variance is unchanged
adding
to every value won't make them more spread out
Sometimes it helps to rewrite expressions into the form
is the same as
Do these rules work for other functions of X?
The expectation formula works for other functions, for example
Note that
does not simplify to
Simplify algebra before taking expectations
The variance formula also works for other functions, for example
Where
means
Simplify algebra before taking variances
Worked Example
is a random variable such that
and
.
Find the value of:
(i)
(ii)
(iii) .

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