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Intersection of Sets

A random vari...

Question

A random variable $X$ has the following probability distribution:
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$
$P (X = x)$ $k$ $3 k$ $5 k$ $7 k$ $9 k$ $11 k$ $13 k$
(a) Find $k$
(b) Find $P (0 < X < 4)$
(c) Obtain cumulative distribution function (c.d.f) of $X$ .

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Solution

(a) $K + 3 K + 5 K + 7 K + 9 K + 11 K + 13 K = 1$
$∴$ $49 K = 1$
$∴$ $K = \frac{1}{49}$
(b) $P (0 < x < 4) = P (1) + P (2) + P (3)$
$\frac{3}{49} + \frac{10}{49} + \frac{21}{49} = \frac{34}{49}$
(c) C.D.F $= (2 x + 1) K, 0 \leq x$

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