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Probability Distribution

The probabili...

Question

The probability distribution of a random variable is given below:
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P (X = x)$ $0$ $K$ $2 K$ $2 K$ $3 K$ $K^{2}$ $2 K^{2}$ $7 K^{2} + K$
Then $P (0 < X < 5) =$

\frac{1}{10}

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\frac{3}{10}

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\frac{8}{10}

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\frac{7}{10}

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Solution

The correct option is B $\frac{8}{10}$
$\sum P (X) = 1$

$\Rightarrow 9 K + 10 K^{2} = 1$

$\Rightarrow 10 K^{2} + 9 K - 1 = 0$
$\Rightarrow 10 K^{2} + 10 K - K - 1 = 0$

$\Rightarrow 10 K (K + 1) - 1 (K + 1) = 0$
$\Rightarrow K = \frac{1}{10}, - 1$ (rejected)

$∴ P (0 < X < 5) = P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)$
$= 8 K$
$= \frac{8}{10}$

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