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Complement of an Event

A random vari...

Question

A random variable x has the following probability function:

x 0 1 3 4 5 6 7

P(x) 0 K 2K 2K 3K $K^{2}$ 7 K $^{2}$ +K

then $P (0 < x < 5)$ is _________
0.51

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Solution

The correct option is A 0.51
If x is a random variable then $\sum P (x_{i)} = 1$ i.e,

$0 + K + 2 K + 2 K + 3 K + K^{2} + 7 K^{2} + K = 1$
$9 K + 8 K^{2} = 1$
or $8 K^{2} + 9 K - 1 = 0$

$∴$ $K = \frac{- 9 \pm \sqrt{81 + 32}}{16} = 0.102$ (Taking positive sign)

$P (0 < x < 5) = P (x = 1) + P (x = 3) + P (x = 4)$
$= K + 2 K + 2 K = 5 K$
$= 5 \times 0.102 = 0.51$

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