The discrete random variables X and Y are independent from one another and are defined as X ~ B 16 , 0 . 25…

Given,

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X~B\left(16,0.25\right)$ and $Y~P\left(2\right)$,

Now given for $X$, $n=16$ and $p=0.25, \text{so} q=1-0.25=0.75$,

Now variance is given by $npq=16\times 0.25\times 0.75=3$

And variance of $Y$ is given as $2$,

So sum of variance of $X \& Y$ is given by $3+2=5$