The probability distribution function oif a random variable X is … - Vidyadip

Question

The probability distribution function oif a random variable $X$ is given by

$X_i$	$0$	$1$	$2$
$P_i$	$3c^3$	$4c - 10c^2$	$5c - 1$

Where $c > 0$
Find: $P(X < 2).$

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Answer

$\text{P}(\text{X}<2)=\text{P}(0)+\text{P}(1)$
$=3\text{c}^3+4\text{c}-10\text{c}^2$
$=3\Big(\frac{1}{3}\Big)^3+4\Big(\frac{1}{3}\Big)-10\Big(\frac{1}{3}\Big)^2$
$=\frac{3}{27}+\frac{4}{3}-\frac{10}{9}$
$=\frac{1}{9}+\frac{4}{3}-\frac{10}{9}$
$=\frac{3}{9}$
$\therefore\ \text{P}(\text{x}<2)=\frac{1}{3}$

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