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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 C $\frac{8}{10}$
$\sum p (X = x_{i}) = 1$

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

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

$10 K^{2} + 10 k - k - 1 = 0$

$10 K (K + 1) - 1 (K + 1) = 0$

$K = \frac{1}{10}$

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

$∴ P (0 < X < 5) = \frac{8}{10}$

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P (0 < X < 5) =

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