A discrete random variable X has the probability distribution giv… - Vidyadip

Question

A discrete random variable $X$ has the probability distribution given below:

$X:$	$0.5$	$1$	$1.5$	$2$
$P(X):$	$k$	$k^2$	$2k^2$	$k$

Find the value of $k.$

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Answer

We know that,
$P(0.5) + P(1) + P(1.5) + P(2) = 1$
$k + k^2+ 2k^2 + k = 1$
$3k^2 + 2k - 1 = 0$
$3k^2 + 3k - k - 1 = 0$
$(3k - 1)(k + 1) = 0$
$\text{k}=\frac{1}{3}$ or $\text{k}=-1$
We know that $0\leq\text{P}(\text{X})\leq1$
$\therefore\ \text{k}=\frac{1}{3}$

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