Question

The probability distribution of a random variable is given below.

Answer 1

Step 1:

Write the range of the probability of any event

`\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}`

Step 2

`\begin{gathered} \sum ^3_0\text{ p(x) = }0\text{ + a + 4a + 9a = 14a} \\ 14a\text{ = 1} \\ \text{a = }(1)/(14) \end{gathered}`

Step 3:

`\begin{gathered} \text{Expected value } \\ =\sum ^3_0x\mathrm{}p(x) \\ =\text{ 0}*0\text{ + }1* a\text{ + 2}*4a\text{ + 3}*9a \\ \text{= 0 + a + 8a + 27a} \\ =\text{ 36a} \\ =\text{ 36}*\text{ }(1)/(14) \\ =(36)/(14) \\ =\text{ 2.57} \end{gathered}`
`\begin{gathered} Final\text{ answer} \\ (1)/(14)|2.57 \end{gathered}`

Option C