Question 6 - A-Level Maths

Exam Board	Edexcel
Module	S1 (Statistics 1)
Year	2011
Session	January
Topic	Discrete Probability Distributions
Type	Probabilities in table form with k

\(x\)	1	2	3	4
\(\mathrm { P } ( X = x )\)	\(k\)	\(2 k\)	\(3 k\)	\(4 k\)

Show that \(k = 0.1\) Find
\(\mathrm { E } ( X )\)
\(\mathrm { E } \left( X ^ { 2 } \right)\)
\(\operatorname { Var } ( 2 - 5 X )\) Two independent observations \(X _ { 1 }\) and \(X _ { 2 }\) are made of \(X\).
Show that \(\mathrm { P } \left( X _ { 1 } + X _ { 2 } = 4 \right) = 0.1\)
Complete the probability distribution table for \(X _ { 1 } + X _ { 2 }\)
\(y\) 2 3 4 5 6 7 8
\(\mathrm { P } \left( X _ { 1 } + X _ { 2 } = y \right)\) 0.01 0.04 0.10 0.25 0.24
Find \(\mathrm { P } \left( 1.5 < X _ { 1 } + X _ { 2 } \leqslant 3.5 \right)\)

\(y\)	2	3	4	5	6	7	8
\(\mathrm { P } \left( X _ { 1 } + X _ { 2 } = y \right)\)	0.01	0.04	0.10		0.25	0.24