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Probability Distribution

A random vari...

Question

A random variable $X$ has the probability distribution,
$X = x$ $- 2$ $- 1$ $0$ $1$ $2$ $3$
$P (x)$ $\frac{1}{10}$ $K$ $\frac{1}{5}$ $2 K$ $\frac{3}{10}$ $K$

\frac{2}{10}

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\frac{1}{10}

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\frac{3}{10}

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\frac{7}{10}

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Solution

The correct option is C $\frac{1}{10}$
The sum of probability of all the possible outcomes should be $1$ .

That is $\sum P (x_{i}) = 1$

$⟹ \frac{1}{10} + K + \frac{1}{5} + 2 K + \frac{3}{10} + K = 1$

$⟹ 4 K + \frac{6}{10} = 1$

$⟹ 4 K = 1 - \frac{6}{10} = \frac{4}{10}$

$⟹ K = \frac{1}{10}$

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