Step 1:
Write the range of the probability of any event
[tex]\begin{gathered} \text{Probability of any event is in the range of } \\ 0\leq\text{ P(event) }\leq\text{ 1} \\ \text{Total probability = 1} \end{gathered}[/tex]
Step 2
[tex]\begin{gathered} \sum ^3_0\text{ p(x) = }0\text{ + a + 4a + 9a = 14a} \\ 14a\text{ = 1} \\ \text{a = }\frac{1}{14} \end{gathered}[/tex]
Step 3:
[tex]\begin{gathered} \text{Expected value } \\ =\sum ^3_0x\mathrm{}p(x) \\ =\text{ 0}\times0\text{ + }1\times a\text{ + 2}\times4a\text{ + 3}\times9a \\ \text{= 0 + a + 8a + 27a} \\ =\text{ 36a} \\ =\text{ 36}\times\text{ }\frac{1}{14} \\ =\frac{36}{14} \\ =\text{ 2.57} \end{gathered}[/tex][tex]\begin{gathered} Final\text{ answer} \\ \frac{1}{14}|2.57 \end{gathered}[/tex]
Option C
