Question 6 - A-Level Maths

Exam Board	OCR MEI
Module	S1 (Statistics 1)
Year	2015
Session	June
Topic	Discrete Probability Distributions
Type	Construct distribution then calculate probability

6 Three fair six-sided dice are thrown. The random variable \(X\) represents the highest of the three scores on the dice.

Show that \(\mathrm { P } ( X = 6 ) = \frac { 91 } { 216 }\). The table shows the probability distribution of \(X\).
\(r\) 1 2 3 4 5 6
\(\mathrm { P } ( X = r )\) \(\frac { 1 } { 216 }\) \(\frac { 7 } { 216 }\) \(\frac { 19 } { 216 }\) \(\frac { 37 } { 216 }\) \(\frac { 61 } { 216 }\) \(\frac { 91 } { 216 }\)
Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).

\(r\)	1	2	3	4	5	6
\(\mathrm { P } ( X = r )\)	\(\frac { 1 } { 216 }\)	\(\frac { 7 } { 216 }\)	\(\frac { 19 } { 216 }\)	\(\frac { 37 } { 216 }\)	\(\frac { 61 } { 216 }\)	\(\frac { 91 } { 216 }\)