A random variable X has the following distribution :
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(X) | 0 | $3k$ | $k$ | $2k$ | $3k^2$ | $k^2$ | $6k^2$ | $3k$ |
The value of k is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{1}{10}$
$∑P_i(x_i)=1$
$9k+10k^2=1$
$10k^2+9k-1=0$
$10k^2+10k-k-1=0$
$10k(k+1)-1(k+1)=0$
$(10k-1)(k+1)=0$
so $k=\frac{1}{10}$ as $k≠-1$