The Probability distribution of a random variable X is given as :
| X: | 0 | 1 | 2 | 3 | 4 |
| P(X): | K | 2K | 4K | 5K | 7K |
The mean of the distribution is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{53}{19}$
The sum of all probabilities,
$k+2k+4k+5k+7k=1$
$19k=1$
$k=\frac{1}{19}$
The mean or expected value is,
$E(X)=\sum\limits_{x}P(X=x)x$
$=0+\frac{2}{19}+\frac{8}{19}+\frac{15}{19}+\frac{28}{19}$
$=\frac{53}{19}$