The probability distribution of a discrete random variable $X$ is:
$X = x$ $1$ $2$ $3$ $4$ $5$
$P (X = x)$ $k$ $2 k$ $3 k$ $4 k$ $5 k$
Find $P (X \leq 4)$

\frac{2}{3}

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\frac{3}{4}

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\frac{4}{5}

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\frac{5}{6}

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Solution

The correct option is A $\frac{2}{3}$
Here, we must have $k + 2 k + 3 k + 4 k + 5 k = 1$
$\Rightarrow 15 k = 1$
$\Rightarrow k = \frac{1}{15}$
Now, $P (X \leq 4) = k + 2 k + 3 k + 4 k$
$= \frac{1}{15} + \frac{2}{15} + \frac{3}{15} + \frac{4}{15}$
$= \frac{10}{15}$
$∴ P (X \leq 4) = \frac{2}{3}$

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P (2 \leq x < 5) =

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