Question 3 - A-Level Maths

Exam Board	Edexcel
Module	FS1 AS (Further Statistics 1 AS)
Year	2021
Session	June
Topic	Discrete Random Variables
Type	Expectation and variance from distribution

$x$	- 3	- 2	- 1	0	2	5
$\mathrm { P } ( X = x )$	0.3	0.15	0.1	0.15	0.1	0.2

Find $\mathrm { E } ( X )$ Given that $\operatorname { Var } ( X ) = 8.79$
find $\mathrm { E } \left( X ^ { 2 } \right)$ The discrete random variable $Y$ has probability distribution
$y$ - 2 - 1 0 1 2
$\mathrm { P } ( Y = y )$ $3 a$ $a$ $b$ $a$ $c$
where $a$, $b$ and $c$ are constants.
For the random variable $Y$ $$\mathrm { P } ( Y \leqslant 0 ) = 0.75 \quad \text { and } \quad \mathrm { E } \left( Y ^ { 2 } + 3 \right) = 5$$
Find the value of $a$, the value of $b$ and the value of $c$ The random variable $W = Y - X$ where $Y$ and $X$ are independent.
The random variable $T = 3 W - 8$
Calculate $\mathrm { P } ( W > T )$

\(y\)	- 2	- 1	0	1	2
\(\mathrm { P } ( Y = y )\)	\(3 a\)	\(a\)	\(b\)	\(a\)	\(c\)

\(x\)	- 3	- 2	- 1	0	2	5
\(\mathrm { P } ( X = x )\)	0.3	0.15	0.1	0.15	0.1	0.2