A random variable ' X ' has the following probability distributio… - Vidyadip

MCQ

A random variable ' X ' has the following probability distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	2k	2k	3k	$k ^2$	2$k ^2$	7$k ^2$	2k

The value of $k$ is

A
-1
B
1
C
$-\frac{1}{10}$
✓
$\frac{1}{10}$

✓

Answer

Correct option: D.

$\frac{1}{10}$

(D) $\frac{1}{10}$
Explanation: $0+2 \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}+\mathrm{k}^{2}+2 \mathrm{k}^{2}+7 \mathrm{k}^{2}+2 \mathrm{k}=1$
$\Rightarrow 10 \mathrm{k}^{2}+9 \mathrm{k}-1=0 \Rightarrow(10 \mathrm{k}-1)(\mathrm{k}+1)=0$
$\Rightarrow k=\frac{1}{10},-1$ but $\mathrm{k} \neq-1$
$\Rightarrow k=\frac{1}{10}$

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