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, $\sum_{i=1}^\pi P_i=1$, where $P_i \geq 0$
$\begin{array}{l}\Rightarrow P_1+P_2+P_3+P_1=1 \\ \Rightarrow k+k^2+2 k^2+k=1 \\ \Rightarrow 3 k^2+2 k-1=0 \\ \Rightarrow(3 k-1)(k+1)=0 \\ \Rightarrow k=\frac{1}{3} .\quad\quad\quad(\text{as k is}\geq0)\end{array}$

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