Question 1 - A-Level Maths

Exam Board	OCR
Module	S1 (Statistics 1)
Year	2009
Session	January
Topic	Discrete Probability Distributions
Type	Verify probability from independent trials

1 Each time a certain triangular spinner is spun, it lands on one of the numbers 0,1 and 2 with probabilities as shown in the table.

The spinner is spun twice. The total of the two numbers on which it lands is denoted by \(X\).

Show that \(\mathrm { P } ( X = 2 ) = 0.18\). The probability distribution of \(X\) is given in the table.
\(x\) 0 1 2 3 4
\(\mathrm { P } ( X = x )\) 0.49 0.28 0.18 0.04 0.01
Calculate \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).

\(x\)	0	1	2	3	4
\(\mathrm { P } ( X = x )\)	0.49	0.28	0.18	0.04	0.01