If the probability distribution of a random variable X is as given below:
| X=x: | -2 | -1 | 0 | 1 | 2 | 3 |
| P(X+x): | $\frac{1}{10}$ | k | $\frac{1}{5}$ | 2k | $\frac{3}{10}$ | k |
The the value of k, is
Answer & explanation
Correct answer: option 1
The given distribution is a probability distribution.
$∴ P(X=-2)+P(X=-1)+P(X=0)+P(X=1)+P(X=2)+P(X+3)=1$
$⇒ \frac{1}{10}+k+\frac{1}{5}+2k +\frac{3}{10}+ k = 1⇒4k =\frac{4}{10}⇒ k = \frac{1}{10}$