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Probability Distribution

A random vari...

Question

A random variable $x$ has the following probability distribution:
$x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$
$P (X = x)$ $k$ $3 k$ $5 k$ $7 k$ $9 k$ $11 k$ $13 k$
Find $^{'} k^{'}$ .

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Solution

$x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$
$P (X = x)$ $k$ $3 k$ $5 k$ $7 k$ $9 k$ $11 k$ $13 k$
We know,

$6 \sum r = 0 P (X = x) = 1$

$∴ k + 3 k + 5 k + 7 k + 9 k + 11 k + 13 k = 1$

$49 k = 1$

$k = \frac{1}{49}$

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