A random variable X has the following probability distribution: X… - Vidyadip

MCQ

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

X	0	1	2	3	4	5	6	7
P(X)	0	P	2P	2P	3P	$\mathrm{P}^2$	$2 \mathrm{P}^2$	$7 \mathrm{P}^2+\mathrm{P}$

The value of P is

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

✓

Answer

Correct option: B.

$\frac{1}{10}$

(B)
$ \text {Since, } \sum_{x=0}^7 \mathrm{P}(\mathrm{X}=x)=1$
$\begin{aligned} & \therefore 0+\mathrm{P}+2 \mathrm{P}+2 \mathrm{P}+3 \mathrm{P}+\mathrm{P}^2+2 \mathrm{P}^2+7 \mathrm{P}^2+\mathrm{P}=1 \\ & \therefore 10 \mathrm{P}^2+9 \mathrm{P}-1=0 \\ & \therefore(\mathrm{P}+1)(10 \mathrm{P}-1)=0 \\ & \therefore \mathrm{P}=\frac{1}{10} \ldots[\because \mathrm{P} \geq 0, \mathrm{P}+1 \neq 0]\end{aligned}$

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