For the given probability distribution :
| X | 5 | 4 | 3 | -3 |
| P(X) | A | $\frac{2}{3}A$ | $\frac{4}{27}$ | $\frac{8A}{9}$ |
If mean $=\frac{19}{9}, $ then the value of constant A will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{1}{3}$
Since, sum of all probabilities must be 1.
$A+\frac{2}{3}A+\frac{4}{27}+\frac{8A}{9}=1$
$⇒A\left(\frac{9+6+8}{9}\right)=1-\frac{4}{27}=\frac{23}{27}$
$⇒A×\frac{23}{9}=\frac{23}{27}$
$⇒A=\frac{9}{27}=\frac{1}{3}$