If the probability distribution of a random variable X is as follows, then $\mathrm{k}=$…
If the probability distribution of a random variable X is as follows, then $\mathrm{k}=$
\begin{array}{|c|c|c|c|c|}\hline \boldsymbol{X}=\boldsymbol{x} & 1 & 2 & 3 & 4 \\\hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & 2 k & 4 k & 3 k & k \\\hline\end{array}
$\frac{1}{10}$
$\frac{2}{10}$
$\frac{3}{10}$
$\frac{4}{10}$
Solution
We know that
$\begin{aligned} & \Sigma P_i=1 \Rightarrow 2 k+4 k+3 k+k=1 \\ & \Rightarrow 10 k=1 \Rightarrow k=\frac{1}{10}\end{aligned}$